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  • 1
    Digitale Medien
    Digitale Medien
    Unsteady convection and convection-diffusion problems via direct overlapping domain decomposition methods (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 387-406 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In solving unsteady problems,domain decomposition methods may be used either for iterative preconditioning each global implicit time-step or directly (noniteratively) within a blockwise implicit time-stepping procedure, in the latter case, the inner boundary values for the subproblems are generated by explicit time-extrapolation. The overlapping variants of this method have been proved to be efficient tools for solving parabolic and first-order hyperbolic problems on modern parallel computers, because they require global communication only once per time-step. The mechanism making this possible is the exponential decay in space of the time-discrete Green's function. We investigate several model problems of convection and convection-diffusion. Favorable optimal and far-reaching estimates of the overlap required have been established in the case of exemplary standard upwind finite-difference schemes. In particular, it has been shown that the overlap for the convection-diffusion problem is the additive function of overlaps for the corresponding convection and diffusion problem to be considered independently. These results have been confirmed with several numerical test examples. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 387-406, 1998
    Zusätzliches Material: 8 Ill.
    Materialart: Digitale Medien
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  • 2
    Digitale Medien
    Digitale Medien
    A first-second order splitting method for a third-order partial differential equation (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 89-96 
    Details
    ISSN: 0749-159X
    Schlagwort(e): finite element method ; third-order differential equation ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A splitting of a third order partial differential equation into a first-order and a second-order one is proposed as the basis for a mixed finite element method to approximate its solution. A time-continuous numerical method is described and error estimates for its solution are demonstrated. Finally, a full discretization is described based on backward Euler finite differences in time, and error estimates for the resulting approximation are established. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 89-96, 1998
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  • 3
    Digitale Medien
    Digitale Medien
    Galerkin discontinuous approximation of the transport equation and viscoelastic fluid flow on quadrilaterals (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 97-114 
    Details
    ISSN: 0749-159X
    Schlagwort(e): non-Newtonian fluids ; finite elements ; error estimates ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Numerical simulation of industrial processes involving viscoelastic liquids is often based on finite element methods on quadrilateral meshes. However, numerical analysis of these methods has so far been limited to triangular meshes. In this work, we consider quadrilateral meshes. We first study the approximation of the transport equation by a Galerkin discontinuous method and prove an O(hk+1/2) error estimates for the Qk finite element. Then we study a differential model for viscoelastic flow with unknowns u the velocity, p the pressure, and σ the viscoelastic part of the extra-stress tensor. The approximations are ((Q1)2 transforms of) Qk+1 continuous for u, Qk discontinuous for σ, and Pk discontinuous for p, with k ≥ 1. Upwinding for σ is obtained by the Galerkin discontinuous method. We show that an error estimate of order O(hk+1/2) is valid in the energy norm for the three unknowns. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 97-114, 1998
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  • 4
    Digitale Medien
    Digitale Medien
    Stabilized spectral element approximation for the Navier-Stokes equations (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 115-141 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Navier-Stokes equations ; spectral elements ; stabilization techniques ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The conforming spectral element methods are applied to solve the linearized Navier-Stokes equations by the help of stabilization techniques like those applied for finite elements. The stability and convergence analysis is carried out and essential numerical results are presented demonstrating the high accuracy of the method as well as its robustness. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 115-141, 1998
    Zusätzliches Material: 11 Ill.
    Materialart: Digitale Medien
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  • 5
    Digitale Medien
    Digitale Medien
    Spectral approximation in the numerical stability study of nondivergent viscous flows on a sphere (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 143-157 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Normal mode stability ; spectral approximation ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The accuracy of calculating the normal modes in the numerical linear stability study of two-dimensional nondivergent viscous flows on a rotating sphere is analyzed. Discrete spectral problems are obtained by truncating Fourier's series of the spherical harmonics for both the basic flow and the disturbances to spherical polynomials of degrees K and N, respectively. The spectral theory for the closed operators [1], and embedding theorems for the Hilbert and Banach spaces of smooth functions on a sphere are used to estimate the rate of convergence of the eigenvalues and eigenvectors. It is shown that the convergence takes place if the basic state is sufficiently smooth, and the truncation numbers K and N of Fourier's series for the basic flow and disturbances tend to infinity keeping the ratio N/K fixed. The convergence rate increases with the smoothness of the basic flow and with the power s of the Laplace operator in the vorticity equation diffusion term. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:143-157, 1998
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  • 6
    Digitale Medien
    Digitale Medien
    A second-order ADI scheme for three-dimensional parabolic differential equations (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 159-168 
    Details
    ISSN: 0749-159X
    Schlagwort(e): ADI scheme ; parabolic differential equation ; stability ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A second-order unconditionally stable ADI scheme has been developed for solving three-dimensional parabolic equations. This scheme reduces three-dimensional problems to a succession of one-dimensional problems. Further, the scheme is suitable for simulating fast transient phenomena. Numerical examples show that the scheme gives an accurate solution for the parabolic equation and converges rapidly to the steady state solution. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:159-168, 1998
    Zusätzliches Material: 4 Ill.
    Materialart: Digitale Medien
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  • 7
    Digitale Medien
    Digitale Medien
    A two-stage least-squares finite element method for the stress-pressure-displacement elasticity equations (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 297-315 
    Details
    ISSN: 0749-159X
    Schlagwort(e): elasticity equations ; least-squares ; finite elements ; error estimates ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A new stress-pressure-displacement formulation for the planar elasticity equations is proposed by introducing the auxiliary variables, stresses, and pressure. The resulting first-order system involves a nonnegative parameter that measures the material compressibility for the elastic body. A two-stage least-squares finite element procedure is introduced for approximating the solution to this system with appropriate boundary conditions. It is shown that the two-stage least-squares scheme is stable and, with respect to the order of approximation for smooth exact solutions, the rates of convergence of the approximations for all the unknowns are optimal both in the H1-norm and in the L2-norm. Numerical experiments with various values of the parameter are examined, which demonstrate the theoretical estimates. Among other things, computational results indicate that the behavior of convergence is uniform in the nonnegative parameter. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 297-315, 1998
    Zusätzliches Material: 4 Tab.
    Materialart: Digitale Medien
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  • 8
    Digitale Medien
    Digitale Medien
    Monotone iterations for numerical solutions of reaction-diffusion-convection equations with time delay (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 339-351 
    Details
    ISSN: 0749-159X
    Schlagwort(e): monotone iteration ; finite difference equation ; reaction-diffusion-convection ; time delay ; upper and lower solutions ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this article we use the monotone method for the computation of numerical solutions of a nonlinear reaction-diffusion-convection problem with time delay. Three monotone iteration processes for a suitably formulated finite-difference system of the problem are presented. It is shown that the sequence of iteration from each of these iterative schemes converges from either above or below to a unique solution of the finite-difference system without any monotone condition on the nonlinear reaction function. An analytical comparison result among the three processes of iterations is given. Also given is the application of the iterative schemes to some model problems in population dynamics, including numerical results of a model problem with known analytical solution. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 339-351, 1998
    Zusätzliches Material: 2 Ill.
    Materialart: Digitale Medien
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  • 9
    Digitale Medien
    Digitale Medien
    A numerical method for the first-order wave equation with discontinuous initial data (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 353-365 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Euler equations ; contact discontinuity ; finite difference schemes ; dispersion ; first-order wave equation ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We introduce a method, constructed such that numerical solutions of the wave equation are well behaved when the solutions also contain discontinuities. The wave equation serves as a model problem for the Euler equations when the solution contains a contact discontinuity. Numerical computations of linear equations and the Euler equations in one and two dimensions are presented. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 353-365, 1998
    Zusätzliches Material: 4 Ill.
    Materialart: Digitale Medien
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  • 10
    Digitale Medien
    Digitale Medien
    Superconvergence in the projected-shear plate-bending finite element method (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 367-386 
    Details
    ISSN: 0749-159X
    Schlagwort(e): finite element methods ; superconvergence ; the Reissner-Mindlin plate ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A projected-shear finite element method for periodic Reissner-Mindlin plate model are analyzed for rectangular meshes. A projection operator is applied to the shear stress term in the bilinear form. Optimal error estimates in the L2-norm, the H1-norm, and the energy norm for both displacement and rotations are established and gradient superconvergence along the Gauss lines is justified in some weak senses. All the convergence and superconvergence results are uniform with respect to the thickness parameter t. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 367-386, 1998
    Zusätzliches Material: 1 Ill.
    Materialart: Digitale Medien
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  • 11
    Digitale Medien
    Digitale Medien
    Global and domain-decomposed mixed methods for the solution of Maxwell's equations with application to magnetotellurics (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 407-437 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Maxwell's equations ; magnetotellurics ; domain decomposition ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A collection of global and domain decomposition mixed finite element schemes for the approximate solution of the harmonic Maxwell's equations on a bounded domain with absorbing boundary conditions at the artificial boundaries are presented. The numerical procedures allow us to solve efficiently the direct problem in magnetotellurics consisting of determining the electromagnetic scattered field in a two-dimensional earth model of arbitrary conductivity properties. Convergence results for the numerical procedures are derived. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 407-437, 1998
    Zusätzliches Material: 1 Ill.
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  • 12
    Digitale Medien
    Digitale Medien
    The coupling of boundary integral and finite element methods for the nonstationary exterior flow (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 549-565 
    Details
    ISSN: 0749-159X
    Schlagwort(e): boundary integral ; finite element ; Navier-Stokes equations ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this article, we represent a new numerical method for solving the nonstationary Navier-Stokes equations in an unbounded domain. The technique consists of coupling the boundary integral and the finite element method. The variational formulation and the well-posedness of the coupling method are obtained. The convergence and optimal error estimates for the approximate solution are provided. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 549-565, 1998
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  • 13
    Digitale Medien
    Digitale Medien
    Numerical analysis of finite element methods for miscible displacements in porous media (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 519-548 
    Details
    ISSN: 0749-159X
    Schlagwort(e): miscible displacements ; finite elements ; error estimates ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Finite element methods are used to solve a coupled system of nonlinear partial differential equations, which models incompressible miscible displacement in porous media. Through a backward finite difference discretization in time, we define a sequentially implicit time-stepping algorithm that uncouples the system at each time-step. The Galerkin method is employed to approximate the pressure, and accurate velocity approximations are calculated via a post-processing technique involving the conservation of mass and Darcy's law. A stabilized finite element (SUPG) method is applied to the convection-diffusion equation delivering stable and accurate solutions. Error estimates with quasi-optimal rates of convergence are derived under suitable regularity hypotheses. Numerical results are presented confirming the predicted rates of convergence for the post-processing technique and illustrating the performance of the proposed methodology when applied to miscible displacements with adverse mobility ratios. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 519-548, 1998
    Zusätzliches Material: 6 Ill.
    Materialart: Digitale Medien
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  • 14
    Digitale Medien
    Digitale Medien
    Finite differences on triangular grids (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 567-579 
    Details
    ISSN: 0749-159X
    Schlagwort(e): finite difference ; finite element ; triangular grid ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We define a finite differences method for triangular grids and we show how to link it to a finite element method. From this new point of view we then analyze properties of the solution and convergence. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 567-579, 1998
    Zusätzliches Material: 5 Ill.
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  • 15
    Digitale Medien
    Digitale Medien
    Symbolic derivation of finite difference approximations for the three-dimensional Poisson equation (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 593-606 
    Details
    ISSN: 0749-159X
    Schlagwort(e): finite difference approximations ; Poisson equation ; symbolic computation ; Mathematica ; three-dimensions ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A symbolic procedure for deriving various finite difference approximations for the three-dimensional Poisson equation is described. Based on the software package Mathematica, we utilize for the formulation local solutions of the differential equation and obtain the standard second-order scheme (7-point), three fourth-order finite difference schemes (15-point, 19-point, 21-point), and one sixth-order scheme (27-point). The symbolic method is simple and can be used to obtain the finite difference approximations for other partial differential equations. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 593-606, 1998
    Zusätzliches Material: 1 Ill.
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  • 16
    Digitale Medien
    Digitale Medien
    Applications of a space decomposition method to linear and nonlinear elliptic problems (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 717-737 
    Details
    ISSN: 0749-159X
    Schlagwort(e): parallel ; domain decomposition ; nonlinear ; elliptic equation ; space decomposition ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: This work presents some space decomposition algorithms for a convex minimization problem. The algorithms has linear rate of convergence and the rate of convergence depends only on four constants. The space decomposition could be a multigrid or domain decomposition method. We explain the detailed procedure to implement our algorithms for a two-level overlapping domain decomposition method and estimate the needed constants. Numerical tests are reported for linear as well as nonlinear elliptic problems. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 717-737, 1998
    Zusätzliches Material: 7 Ill.
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  • 17
    Digitale Medien
    Digitale Medien
    A second-order splitting combined with orthogonal cubic spline collocation method for the Rosenau equation (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 695-716 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Rosenau equation ; orthogonal spline collocation method ; differential algebraic equations (DAEs) ; implicit Runge-Kutta methods ; decay estimates ; BBM (Benjamin-Bona-Mahony) equation ; BBMB (Benjamin-Bona-Mahony-Burgers) equation ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A second-order splitting method is applied to a KdV-like Rosenau equation in one space variable. Then an orthogonal cubic spline collocation procedure is employed to approximate the resulting system. This semidiscrete method yields a system of differential algebraic equations (DAEs) of index 1. Error estimates in L2 and L∞ norms have been obtained for the semidiscrete approximations. For the temporal discretization, the time integrator RADAU5 is used for the resulting system. Some numerical experiments have been conducted to validate the theoretical results and to confirm the qualitative behaviors of the Rosenau equation. Finally, orthogonal cubic spline collocation method is directly applied to BBM (Benjamin-Bona-Mahony) and BBMB (Benjamin-Bona-Mahony-Burgers) equations and the well-known decay estimates are demonstrated for the computed solution. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 695-716, 1998
    Zusätzliches Material: 9 Ill.
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  • 18
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    Digitale Medien
    On the numerical integration of multi-dimensional, initial boundary value problems for the Euler equations in quasi-linear form (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 781-814 
    Details
    ISSN: 0749-159X
    Schlagwort(e): hyperbolic problems ; IBVP ; multi-dimensional ; nonorthogonal mesh ; quasi-linear form ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A matricial formalism to solve multi-dimensional initial boundary values problems for hyperbolic equations written in quasi-linear based on the λ scheme approach is presented. The derivation is carried out for nonorthogonal, moving systems of curvilinear coordinates. A uniform treatment of the integration at the boundaries, when the boundary conditions can be expressed in terms of combinations of time or space derivatives of the primitive variables, is also presented. The methodology is validated against a two-dimensional test case, the supercritical flow through the Hobson cascade n.2, and in three-dimensional test cases such as the supersonic flow about a sphere and the flow through a plug nozzle. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 781-814, 1998
    Zusätzliches Material: 8 Ill.
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  • 19
    Digitale Medien
    Digitale Medien
    A finite difference scheme for traveling wave solutions to Burgers equation (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 815-820 
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    ISSN: 0749-159X
    Schlagwort(e): Burgers equation ; nonstandard finite difference schemes ; traveling waves ; exact solutions ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We construct a finite difference scheme for the ordinary differential equation describing the traveling wave solutions to the Burgers equation. This difference equation has the property that its solution can be calculated. Our procedure for determining this solution follows closely the analysis used to obtain the traveling wave solutions to the original ordinary differential equation. The finite difference scheme follows directly from application of the nonstandard rules proposed by Mickens. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 815-820, 1998
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  • 20
    Digitale Medien
    Digitale Medien
    A model of a homogenized cavity corresponding to a multinozzle droplet generator for continuous ink-jet printers (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 821-842 
    Details
    ISSN: 0749-159X
    Schlagwort(e): homogenization ; asymptotic analysis ; ink-jet printer ; droplet generator ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We modelize the behavior of a vibrating fluid cavity. Small nozzles are uniformly distributed in one direction on a side of the cavity. By means of asymptotic expansion in powers of the smallest dimension of the cavity, including boundary layer terms, we get the convergence of the solution of the three-dimensional problem, as well as the convergence of the solution of the “homogenized” three-dimensional problem towards the solution of the same two-dimensional problem. Numerical experiments have been carried out in order to illustrate the previous theoretical results. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 821-842, 1998
    Zusätzliches Material: 6 Ill.
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  • 21
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    Digitale Medien
    Approximation to a parabolic system modeling the thermoelastic contacts of two rods (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 1-25 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Finite difference ; thermoelastic contact ; nonlinear parabolic system ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this article, we study a sequence of finite difference approximate solutions to a parabolic system, which models two dissimilar rods that may come into contact as a result of thermoelastic expansion. We construct the approximate solutions based on a set of finite difference schemes to the system, and we will prove that the approximate solutions converge strongly to the exact solutions. Moreover, we obtain and prove rigorously the error bound, which measures the difference between the exact solutions and approximate solutions in a reasonable norm. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 1-25, 1998
    Zusätzliches Material: 3 Ill.
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  • 22
    Digitale Medien
    Digitale Medien
    A space decomposition method for parabolic equations (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 27-46 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Parallel ; domain decomposition ; parabolic equation ; space decomposition ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A convergence proof is given for an abstract parabolic equation using general space decomposition techniques. The space decomposition technique may be a domain decomposition method, a multilevel method, or a multigrid method. It is shown that if the Euler or Crank-Nicolson scheme is used for the parabolic equation, then by suitably choosing the space decomposition, only O(| log τ |) steps of iteration at each time level are needed, where τ is the time-step size. Applications to overlapping domain decomposition and to a two-level method are given for a second-order parabolic equation. The analysis shows that only a one-element overlap is needed. Discussions about iterative and noniterative methods for parabolic equations are presented. A method that combines the two approaches and utilizes some of the good properties of the two approaches is tested numerically. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 27-46, 1998
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  • 23
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    Digitale Medien
    Preconditioners for the p-version of the Galerkin method for a coupled finite element/boundary element system (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 47-61 
    Details
    ISSN: 0749-159X
    Schlagwort(e): p-version finite element method ; boundary element method ; interface problem ; preconditioning ; domain decomposition ; additive Schwarz method ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We propose and analyze efficient preconditioners for solving systems of equations arising from the p-version for the finite element/boundary element coupling. The first preconditioner amounts to a block Jacobi method, whereas the second one is partly given by diagonal scaling. We use the generalized minimum residual method for the solution of the linear system. For our first preconditioner, the number of iterations of the GMRES necessary to obtain a given accuracy grows like log2 p, where p is the polynomial degree of the ansatz functions. The second preconditioner, which is more easily implemented, leads to a number of iterations that behave like p log3 p. Computational results are presented to support this theory. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 47-61, 1998
    Zusätzliches Material: 3 Ill.
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  • 24
    Digitale Medien
    Digitale Medien
    Gauss point mass lumping schemes for Maxwell's equations (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 63-88 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Maxwell equations ; edge finite elements ; mass lumping ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Finite element and finite difference methods for approximating the Maxwell system propagate numerical waves with slightly incorrect velocities, and this results in phase error in the computed solution. Indeed this error limits the type of problem that can be solved, because phase error accumulates during the computation and eventually destroys the solution. Here we propose a family of mass-lumped finite element schemes using edge elements. We emphasize in particular linear elements that are equivalent to the standard Yee FDTD scheme, and cubic elements that have superior phase accuracy. We prove theorems that allow us to perform a dispersion analysis of the two common families of edge elements on rectilinear grids. A result of this analysis is to provide some justification for the choice of the particular family we use. We also provide a limited selection of numerical results that show the efficiency of our scheme. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 63-88, 1998
    Zusätzliches Material: 4 Ill.
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  • 25
    Digitale Medien
    Digitale Medien
    Superconvergent recovery of gradients of piecewise linear finite element approximations on non-uniform mesh partitions (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 169-192 
    Details
    ISSN: 0749-159X
    Schlagwort(e): finite element space ; (1 + α˜)-regular mesh partition ; recovered gradient ; superconvergence ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We propose the use of an averaging scheme, which recovers gradients from piecewise linear finite element approximations on the (1 + α˜) - regular triangular elements to gradients of the weak solution of a second-order elliptic boundary value problem in the 2-dimensional space. The recovered gradients, from mid-points of element edges, are superconvergent estimates of the true gradients. This work is an extension of Levine [Levine, IMA J. Numer. Anal. 5, 407 (1985)] and follows some of the ideas therein. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:169-192, 1998
    Zusätzliches Material: 10 Ill.
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  • 26
    Digitale Medien
    Digitale Medien
    Finite volume methods on Voronoi meshes (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 193-212 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Cell-centered finite differences ; upwind approximations ; error estimates ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Two cell-centered finite difference schemes on Voronoi meshes are derived and investigated. Stability and error estimates in a discrete H1-norm for both symmetric and nonsymmetric problems, including convection dominated, are proven. The theoretical results are illustrated with several numerical experiments. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:193-212, 1998
    Zusätzliches Material: 4 Ill.
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  • 27
    Digitale Medien
    Digitale Medien
    Convergence analysis of a finite volume method via a new nonconforming finite element method (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 213-231 
    Details
    ISSN: 0749-159X
    Schlagwort(e): cell-centered finite volume method ; convergence ; finite element method ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The article is devoted to the study of convergence properties of a Finite Volume Method (FVM) using Voronoi boxes for discretization. The approach is based on the construction of a new nonconforming Finite Element Method (FEM), such that the system of linear equations coincides completely with that for the FVM. Thus, by proving convergence properties of the FEM, we obtain similar ones of the FVM. In this article, the investigations are restricted to the Poisson equation. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:213-231, 1998
    Zusätzliches Material: 2 Ill.
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  • 28
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    Digitale Medien
    A numerical method for problems in infinite strips with irregularities extending to infinity (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 233-249 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Infinite domain ; semi-infinite strip ; Dirichlet-to-Neumann ; Finite element ; variable coefficients ; nonlinear elliptic PDEs ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The Dirichlet-to-Neumann (DtN) Finite Element Method is a combined analytic-numerical method for boundary value problems in infinite domains. The use of this method is usually based on the assumption that, in the infinite domain D exterior to the finite computational domain, the governing differential equations are sufficiently simple. In particular, in D it is generally assumed that the equations are linear, homogeneous, and have constant coefficients. In this article, an extension of the DtN method is proposed, which can be applied to elliptic problems with “irregularities” in the exterior domain D, such as (a) inhomogeneities, (b) variable coefficients, and (c) nonlinearities. This method is based on iterative “regularization” of the problem in D, and on the efficient treatment of infinite-domain integrals. Semi-infinite strip problems are used for illustrating the method. Convergence of the iterative process is analyzed both theoretically and numerically. Nonuniformity difficulties and a way to overcome them are discussed. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:233-249, 1998
    Zusätzliches Material: 7 Ill.
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  • 29
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    Digitale Medien
    Moving finite element methods by use of space-time elements: I. Scalar problems (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 251-262 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Moving finite element ; discontinuous Galerkin ; space-time orientation ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: This article deals with moving finite element methods by use of the time-discontinuous Galerkin formulation in combination with oriented space-time meshes. A principle for mesh orientation in space-time based on minimization of the residual, related to adaptive error control via an a posteriori error estimate, is presented. The relation to Miller's moving finite element method is discussed. The article deals with scalar problems; systems will be treated in a companion article. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:251-262, 1998
    Zusätzliches Material: 7 Ill.
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  • 30
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    Digitale Medien
    On convergence and performance of iterative methods with fourth-order compact schemes (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 263-280 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Convection-diffusion equation ; iterative methods ; fourth-order compact discretization schemes ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We study the convergence and performance of iterative methods with the fourth-order compact discretization schemes for the one- and two-dimensional convection-diffusion equations. For the one-dimensional problem, we investigate the symmetrizability of the coefficient matrix and derive an analytical formula for the spectral radius of the point Jacobi iteration matrix. For the two-dimensional problem, we conduct Fourier analysis to determine the error reduction factors of several basic iterative methods and comment on their potential use as the smoothers for the multilevel methods. Finally, we perform numerical experiments to verify our Fourier analysis results. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:263-280, 1998
    Zusätzliches Material: 10 Ill.
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  • 31
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    Digitale Medien
    An accurate semi-analytic finite difference scheme for two-dimensional elliptic problems with singularities (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 281-296 
    Details
    ISSN: 0749-159X
    Schlagwort(e): singularities ; elliptic PDE ; Laplace equation ; high-order Finite Difference Schemes ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A high-order semi-analytic finite difference scheme is presented to overcome degradation of numerical performance when applied to two-dimensional elliptic problems containing singular points. The scheme, called Least-Square Singular Finite Difference Scheme (L-S SFDS), applies an explicit functional representation of the exact solution in the vicinity of the singularities, and a conventional finite difference scheme on the remaining domain. It is shown that the L-S SFDS is “pollution” free, i.e., no degradation in the convergence rate occurs because of the singularities, and the coefficients of the asymptotic solution in the vicinity of the singularities are computed as a by-product with a very high accuracy. Numerical examples for the Laplace and Poisson equations over domains containing re-entrant corners or abrupt changes in the boundary conditions are presented. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 281-296, 1998
    Zusätzliches Material: 9 Ill.
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  • 32
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    Digitale Medien
    Qualitative behavior of numerical solutions to an s-i-s epidemic model (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 317-337 
    Details
    ISSN: 0749-159X
    Schlagwort(e): s-i-s epidemic model ; finite difference ; method of characteristics ; asymptotic behavior ; periodic solution ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A finite difference scheme along the characteristics is used to approximate the solution of an age-dependent s-i-s epidemic model. The global behavior of the discrete solution resulting from the algorithm is investigated. It is shown that a nontrivial discrete periodic solution is generated by a periodic force of infection. Sufficient (and explicit) threshold conditions for the existence and stability of a unique nontrivial periodic solution are given. Results from numerical experiments are presented. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 317-337, 1998
    Zusätzliches Material: 8 Ill.
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  • 33
    Digitale Medien
    Digitale Medien
    Mesh-centered finite differences from nodal finite elements for elliptic problems (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 439-465 
    Details
    ISSN: 0749-159X
    Schlagwort(e): mesh-centered finite differences ; nodal methods ; elliptic problems ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: After it is shown that the classical five-point mesh-centered finite difference scheme can be derived from a low-order nodal finite element scheme by using nonstandard quadrature formulae, higher-order block mesh-centered finite difference schemes for second-order elliptic problems are derived from higher-order nodal finite elements with nonstandard quadrature formulae as before, combined to a procedure known as “transverse integration.” Numerical experiments with uniform and nonuniform meshes and different types of boundary conditions confirm the theoretical predictions, in discrete as well as continuous norms. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 439-465, 1998
    Zusätzliches Material: 3 Ill.
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  • 34
    Digitale Medien
    Digitale Medien
    Nonstandard methods for the convective transport equation with nonlinear reactions (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 467-485 
    Details
    ISSN: 0749-159X
    Schlagwort(e): convection-reaction equations ; Lagrangian methods ; convective flows ; reactive solute transport problems ; exact finite difference schemes ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A new nonstandard Lagrangian method is constructed for the one-dimensional, transient convective transport equation with nonlinear reaction terms. An “exact” time-stepping scheme is developed with zero local truncation error with respect to time. The scheme is based on nonlocal treatment of nonlinear reactions, and when applied at each spatial grid point gives the new fully discrete numerical method. This approach leads to solutions free from the numerical instabilities that arise because of incorrect modeling of derivatives and nonlinear reaction terms. Algorithms are developed that preserve the properties of the numerical solution in the case of variable velocity fields by using nonuniform spatial grids. Effects of different interpolation techniques are examined and numerical results are presented to demonstrate the performance of the proposed new method. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 467-485, 1998
    Zusätzliches Material: 6 Ill.
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  • 35
    Digitale Medien
    Digitale Medien
    A posteriori error estimates for nonlinear problems: Lr, (0, T; W1,ρ (Ω))-error estimates for finite element discretizations of parabolic equations (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 487-518 
    Details
    ISSN: 0749-159X
    Schlagwort(e): A posteriori error estimates ; nonlinear parabolic PDEs ; time-dependent Navier-Stokes equations ; space-time finite elements ; θ-scheme ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Using the abstract framework of [R. Verfürth, Math. Comput. 62, 445-475 (1996)], we analyze a residual a posteriori error estimator for space-time finite element discretizations of parabolic PDEs. The estimator gives global upper and local lower bounds on the error of the numerical solution. The finite element discretizations in particular cover the so-called θ-scheme, which includes the implicit and explicit Euler methods and the Crank-Nicolson scheme. As particular examples we consider scalar quasilinear parabolic PDEs of 2nd order and the time-dependent incompressible Navier-Stokes equations. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 487-518, 1998
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  • 36
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    Digitale Medien
    A note on Hermitian splitting induced relaxation methods for convection-diffusion equations (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 581-591 
    Details
    ISSN: 0749-159X
    Schlagwort(e): iterative methods ; Hermitian splitting ; successive overrelaxation ; convection-diffusion equation ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The solution of the linear system Ax = b by iterative methods requires a splitting of the coefficient matrix in the form A = M - N where M is usually chosen to be a diagonal or a triangular matrix. In this article we study relaxation methods induced by the Hermitian and skew-Hermitian splittings for the solution of the linear system arising from a compact fourth order approximation to the one dimensional convection-diffusion equation and compare the convergence rates of these relaxation methods to that of the widely used successive overrelaxation (SOR) method. Optimal convergence parameters are derived for each method and numerical experiments are given to supplement the theoretical estimates. For certain values of the diffusion parameter, a relaxation method based on the Hermitian splitting converges faster than SOR. For two-dimensional problems a block form of the iterative algorithm is presented. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 581-591, 1998
    Zusätzliches Material: 1 Ill.
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  • 37
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    Digitale Medien
    Discretization of the stationary convection-diffusion-reaction equation (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 607-625 
    Details
    ISSN: 0749-159X
    Schlagwort(e): convection-diffusion-reaction equation ; finite volume method ; exponential scheme ; flux computation ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A finite volume method for the convection-diffusion-reaction equation is presented, which is a model equation in combustion theory. This method is combined with an exponential scheme for the computation of the fluxes. We prove that the numerical fluxes are second-order accurate, uniformly in the local Peclet numbers. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 607-625, 1998
    Zusätzliches Material: 4 Ill.
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  • 38
    Digitale Medien
    Digitale Medien
    Dimensional splitting with front tracking and adaptive grid refinement (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 627-648 
    Details
    ISSN: 0749-159X
    Schlagwort(e): scalar conservation laws ; dimensional splitting ; front tracking ; error bounds ; adaptive grid refinement ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Front tracking in combination with dimensional splitting is analyzed as a numerical method for scalar conservation laws in two space dimensions. An analytic error bound is derived, and convergence rates based on numerical experiments are presented. Numerical experiments indicate that large CFL numbers can be used without loss of accuracy for a wide range of problems. A new method for grid refinement is introduced. The method easily allows for dynamical changes in the grid, using, for instance, the total variation in each grid cell as a criterion for introducing new or removing existing refinements. Several numerical examples are included, highlighting the features of the numerical method. A comparison with a high-resolution method confirms that dimensional splitting with front tracking is a highly viable numerical method for practical computations. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 627-648, 1998
    Zusätzliches Material: 11 Ill.
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  • 39
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    Digitale Medien
    On the linear stability study of zonal incompressible flows on a sphere (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 649-665 
    Details
    ISSN: 0749-159X
    Schlagwort(e): linear stability ; zonal flows ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The normal mode (linear) stability of zonal flows of a nondivergent fluid on a rotating sphere is considered. The spherical harmonics are used as the basic functions on the sphere. The stability matrix representing in this basis the vorticity equation operator linearized about a zonal flow is analyzed in detail using the recurrent formula derived for the nonlinear triad interaction coefficients. It is shown that the zonal flow having the form of a Legendre polynomial Pn(μ) of degree n is stable to infinitesimal perturbations of every invariant set Im with |m| ≥ n. For each zonal number m, Im is here the span of all the spherical harmonics $Y^{m}_{k}(x)$, whose degree k is greater than or equal to m. It is also shown that such small-scale perturbations are stable not only exponentially, but also algebraically. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 649-665, 1998
    Zusätzliches Material: 4 Ill.
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  • 40
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    Digitale Medien
    Least squares methods for Volterra equations and generalizations (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 679-693 
    Details
    ISSN: 0749-159X
    Schlagwort(e): least squares method ; finite element method ; Volterra equation ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this article least squares approximations to Volterra integral equations are considered, both with exact integration and with quadrature. Optimal error estimates are derived, and it is shown that the same order of convergence is obtained in both cases with only modest requirements on the quadrature rule used in the latter. The most important practical setting for least squares is the case of convolution kernels, and these are also studied in this article. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 679-693, 1998
    Zusätzliches Material: 3 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/num.10501
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  • 41
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    Digitale Medien
    The Method of Fundamental Solutions for Stokes flows with a free surface (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 667-678 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Method of fundamental solutions ; elliptic boundary value problems ; Stokes flow ; free surface ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We investigate the use of the Method of Fundamental Solutions (MFS) for solving Stokes flow problems with a free surface. We apply the method to the creeping planar Newtonian extrudate-swell problem and study the effect of the surface tension on the free surface. The results are in good agreement with existing finite element and boundary element solutions. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 667-678, 1998
    Zusätzliches Material: 5 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/num.10500
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  • 42
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    Digitale Medien
    A family of ELLAM schemes for advection-diffusion-reaction equations and their convergence analyses (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 739-780 
    Details
    ISSN: 0749-159X
    Schlagwort(e): advection-diffusion-reaction transport equations ; characteristic methods ; error estimates ; Eulerian-Lagrangian methods ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A family of ELLAM (Eulerian-Lagrangian localized adjoint method) schemes is developed and analyzed for linear advection-diffusion-reaction transport partial differential equations with any combination of inflow and outflow Dirichlet, Neumann, or flux boundary conditions. The formulation uses space-time finite elements, with edges oriented along Lagrangian flow paths, in a time-stepping procedure, where space-time test functions are chosen to satisfy a local adjoint condition. This allows Eulerian-Lagrangian concepts to be applied in a systematic mass-conservative manner, yielding numerical schemes defined at each discrete time level. Optimal-order error estimates and superconvergence results are derived. Numerical experiments are performed to verify the theoretical estimates. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 739-780, 1998
    Zusätzliches Material: 2 Tab.
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  • 43
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    Digitale Medien
    Vacuum and non-vacuum solutions of the quasi-hydrodynamic semiconductor model in thermal equilibrium (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 225-254 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The quasi-hydrodynamical model for bipolar semiconductor devices in thermal equilibrium admits in general solutions for which the non-negative electron- or hole-density is not strict positive. In this paper sufficient conditions depending on the device's data which lead to or prevent vacuum are presented. The transformation of the model equations to a single semilinear elliptic mixed boundary value problem for the electrostatic potential V reduces the vacuum-non-vacuum discussion to an investigation of the range of V. Monotonicity arguments and the employment of local sub- and supersolutions allow to estimate the size as well as the distance from the Dirichlet boundary of the respective vacuum sets. An one-dimensional model is analysed in some detail.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670180304
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  • 44
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    Digitale Medien
    Global existence and blow-up for a system of heat equations with non-linear boundary conditions (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 307-315 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper, we consider non-negative solutions of We prove that if pq ≤ 1 every solution remains bounded, while all solutions blow up in a finite time if pq 〉 1. We also show that if p,q 〉 1, then blow-up can only occur on the boundary.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670180405
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  • 45
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    Digitale Medien
    On the sharp singular limit for slightly compressible fluids (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 295-306 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We consider the equations of motion to slightly compressible fluids and we prove that solutions converge, in the strong norm, to the solution of the equations of motion of incompressible fluids, as the Mach number goes to zero. From a physical point of view this means the following. Assume that we are dealing with a well-specified fluid, so slightly compressible that we assume it to be incompressible. Our result means that the distance between the (continuous) trajectories of the real and of the idealized solution is ‘small’ with respect to the natural metric, i.e. the metric that endows the data space.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670180404
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  • 46
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    Digitale Medien
    Boundary layer resolution in hierarchical plate modelling (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 345-370 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The dimensional reduction of an elliptic model boundary value problem on a thin, plate-like domain of thickness 2d is analysed. A class of lower-dimensional models with variable model orders in the interior and near the boundary of the plate is investigated and it is shown that for a sufficiently large model order in a O(d∣ln d∣)-neighbourhood of the edge the hierarchical models compensate for the boundary layers of the exact solution - in the sense that their asymptotic rate of convergence as d → 0 is the same as the optimal one for compatible, layer-free solutions.
    Zusätzliches Material: 1 Tab.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670180503
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  • 47
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    Digitale Medien
    Similarity solutions of dispersive long-wave equations in two space dimensions (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 789-802 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper, both the direct method and the non-classical Lie approach are applied to reduce the (2 + 1)-dimensional dispersive long wave equations. Nine types of two-dimensional PDE reductions and 13 types of ODE reductions are given. All the known reductions obtained by the classical Lie approach are reobtained as some special cases. Similar to the (1 + 1)-dimensional case, some types of reductions with essential and logarithmic singular characteristic manifolds are allowed although the model is integrable.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670181004
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  • 48
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    Digitale Medien
    On the initial value problem for the Vlasov-Poisson-Fokker-Planck system with initial data in Lp spaces (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 825-839 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper the global existence of weak solutions for the Vlasov-Poisson-Fokker-Planck equations in three dimensions is proved with an L1 ∩ Lp initial data. Also, the global existence of weak solutions in four dimensions with small initial data is studied. A convergence of the solutions is obtained to those built by E. Horst and R. Hunze when the Fokker-Planck term vanishes. In order to obtain the a priori necessary estimates a sequence of approximate problems is introduced. This sequence is obtained starting from a non-linear regulation of the problem together with a linearization via a time retarded mollification of the non-linear term. The a priori bounds are reached by means of the control of the kinetic energy in the approximate sequence of problems. Then, the proof is completed obtaining the equicontinuity properties which allow to pass to the limit.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670181006
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  • 49
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    Digitale Medien
    An explicit solution of the pseudo-hyperbolic initial boundary value problem in a multiply connected region (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 897-925 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: An explicit solution of the pseudo-hyperbolic initial boundary value problem with a mixed boundary condition has been constructed. The problem describes the propagation of non-stationary internal waves in a stratified and rotational fluid. The generation of waves is caused by small oscillations of double-sided plates beginning at time t = 0. Dynamic pressure is specified on one set of plates and this yields the first boundary condition. Normal velocities are specified on another set of plates and this leads to an analogue of the second boundary condition with time derivatives. The solution has been obtained by the method of non-classical time-dependent dynamic potentials. The uniqueness of the solution has been studied.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670181105
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  • 50
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    Digitale Medien
    A discrete velocity coagulation-fragmentation model (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 959-993 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A discrete velocity Boltzmann model is introduced. It is based on two principles: (i) clusters of particles move in a volume V with seven fixed momenta; (ii) clusters may gain or lose particles according to the rules of Becker-Döring cluster equations. The model provides a kinetic representation of evaporation and condensation. Results of numerical experiments are presented.
    Zusätzliches Material: 3 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670181204
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  • 51
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    Digitale Medien
    On a local in time solvability of the Neumann problem of quasilinear hyperbolic parabolic coupled systems (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 1053-1082 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We prove a local in time existence theorem of classical solutions to some coupled system of quasilinear hyperbolic equations and quasilinear parabolic equations with Neumann boundary condition. This coupled system contains a non-linear thermoelastic equation as an important physical example.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670181304
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  • 52
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    Digitale Medien
    On the one- and one-half-dimensional relativistic Vlasov-Fokker-Planck-Maxwell system (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 1013-1040 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper, we study the relativistic Vlasov-Fokker-Planck-Maxwell system in one space variable and two momentum variables. This non-linear system of equations consists of a transport equation for the phase space distribution function combined with Maxwell's equations for the electric and magnetic fields. It is important in modelling distribution of charged particles in the kinetic theory of plasma. We prove the existence of a classical solution when the initial density decays fast enough with respect to the momentum variables. The solution which shares this same decay condition along with its first derivatives in the momentum variables is unique.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670181302
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  • 53
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    Digitale Medien
    A particle method for a self-gravitating fluid: A convergence result (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 1083-1094 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We study an Hamiltonian system of N particles in ∝3 interacting by a short-range repulsive and a long-range attractive potential. It is shown that the empirical measures associated to the positions and velocity of the system converge to the solutions of Euler equations for a self-gravitating fluid, in the limit as the particle number tends to infinity, for a suitable scaling of the interactions.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670181305
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  • 54
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    Digitale Medien
    Periodic optimal control for parabolic Volterra-Lotka type equations (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 127-146 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: This paper considers the optimal harvesting control of a biological species, whose growth is governed by the parabolic diffusive Volterra-Lotka equation. We prove that such equation with L∞ periodic coefficients has an unique positive periodic solution. We show the existence and uniqueness of an optimal control, and under certain conditions, we characterize the optimal control in terms of a parabolic optimality system. A monotone sequence which converges to the optimal control is constructed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670180204
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  • 55
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    Digitale Medien
    Asymptotic characterization of standing waves and of the static limit for a class of wave equations of higher order with a variable coefficient and time-independent incitation (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 147-168 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We consider the equation (-1)m∇m (p∇mu) + ∂t2u = ƒ in ∝n × (0, ∞) for arbitrary positive integers m and n and under the assumptions p - 1, ƒ ∊ C0∞(∝n) and p 〉 0. Even if the differential operator (-1)m∇m (p∇mu) has no eigenvalues, the solution u(x,t) may increase as t → ∞ for 2m ≥ n. For this case, we derive necessary and sufficient conditions for the convergence of u(x,t) as t → ∞. Furthermore, we characterize the functions occurring in these conditions as solutions of the homogeneous static equation (-1)m∇m (p∇mu) = 0, which satisfy appropriate asymptotic conditions at infinity. We also give an asymptotic characterization of the static limit.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670180205
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  • 56
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    Digitale Medien
    Masthead (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995) 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670180401
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  • 57
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    Digitale Medien
    Existence of a solution for a lubrication problem in elastic journal-bearing devices with thin bearing (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 255-266 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A particular elastohydrodynamic lubrication problem is modelled in this work. The presence of elasticity, lubrication and cavitation calls for a non-linear coupled system of variational equations. The existence of a solution is deduced by means of a constructive algorithm that decouples biharmonic equation of the elastic hinged plate and the lubrication-cavitation Elrod-Adams free boundary problem.
    Zusätzliches Material: 3 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670180402
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  • 58
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    Digitale Medien
    Masthead (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995) 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670180501
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  • 59
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    Digitale Medien
    On the bending of plates with transverse shear deformation and mixed periodic boundary conditions (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 337-344 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The method of matched asymptotic expansions is used to find a homogenized problem whose solution is an approximation to the solution of a mixed periodic boundary value problem in the theory of bending of thin elastic plates. A critical size for the fixed parts of the boundary is found such that the boundary condition of the homogenized problem is an intermediate case between that for the clamped edge plate and that for the free boundary plate.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670180502
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  • 60
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    Digitale Medien
    The free boundary problem of a semiconductor in thermal equilibrium (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 387-412 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The quasi-hydrodynamic model for semiconductor devices in thermal equilibrium admits in general solutions for which the electron or hole density vanish. These sets are called vacuum sets. In this paper estimates on the vacuum sets and a first step in the regularity of the free boundary of these sets are presented. Numerical examples, including error estimates for linear finite elements, for the devices diode, bipolar transistor and thyristor indicate that the free boundary is more regular than theoretically predicted.
    Zusätzliches Material: 13 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670180505
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  • 61
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    Digitale Medien
    Thermal deformations of inhomogeneous elastic plates (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 423-436 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We consider thermal deformations of transversally inhomogenous elastic plates. Thin plate equations are derived as limits of full three-dimensional models both in the linear as well as in the non-linear case with appropriate convergence proofs. In the non-linear case also the corresponding von Kármán equations are formulated. It is obtained that the inhomogeneity leads to the loss of some symmetry properties at the von Kármán equations.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670180602
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  • 62
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    Digitale Medien
    Masthead (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995) 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670180701
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  • 63
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    Digitale Medien
    The double layer potential method for a boundary transmission problem for the Laplace operator in an infinite wedge (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 515-528 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: This paper is concerned with the solution of a boundary transmission problem in an infinite wedge. We treat this problem by a boundary integral method using Green's contact function for two half-spaces. The integral operators are studied via a harmonic analysis approach which goes back to a paper of Fabes et al. We improve their results studying the Fourier symbol of the associated integral operators on the half-plane. This leads to invertibility criteria for the boundary integral operators.
    Zusätzliches Material: 1 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670180703
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  • 64
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    Digitale Medien
    Masthead (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995) 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670180801
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  • 65
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    About the concept of measure-valued solutions to distributed parameter systems (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 671-685 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The measure-valued (mv) solutions are commonly defined in the literature simply by putting Young measures into the respective partial differential equations. Here a few examples of mv-solutions to evolution problems (conservation laws, fluid dynamics and a so-called backward-forward heat problem) are re-investigated to show that such definitions are not satisfactorily selective, i.e. they admit (sometimes surprisingly) many mv-solutions apparently without any physical sense. Then an attempt for a selective definition in the case of the backward-forward heat problem is made, resulting to a certain evolution variational inequality.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670180902
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  • 66
    Digitale Medien
    Digitale Medien
    Masthead (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995) 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670181001
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  • 67
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    A new system of boundary integral equations for plates with free edges (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 755-772 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We present a new system of boundary integral equations for the free-edge plate. This system expresses an abstract symmetric variational problem posed on the boundary of the plate. In order to obtain this abstract problem, we must set the exterior boundary value problem corresponding to the free-edge plate in a framework of weighted Sobolev spaces. Finally, we take care of the hypersingular kernels appearing in our system of BIEs, by using an abstract technique of integration by parts.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670181002
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  • 68
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    Digitale Medien
    The sorption of mixtures under linear equilibrium partitioning and chemical transformation (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 803-823 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We consider the flow of a mixture, whose components are undergoing temporally and spatially varying linear equilibrium sorption partitioning and, possibly nonlinear, chemical transformations. We are able to generate an evolution system of parabolic type on the space of uniformly continuous functions and thus obtain classical solutions for arbitrary initial values.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670181005
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  • 69
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    Digitale Medien
    Large time asymptotics for a class of wave equations of higher order with a variable coefficient and time-independent incitation (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 1-25 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We consider the equation (-1)m∇m (p∇mu) + ∂t2u = ƒ in ∝n × [0, ∞] for arbitrary positive integers m and n and under the assumptions p -1, ƒ ∊ C0∞ and p 〉 0. Under the additional assumption that the differential operator (-1)m∇m (p∇mu) has no eigenvalues we derive an asymptotic expansion for u(x,t) as t → including all terms up to order o(1). In particular, we show that for 2m ≥ n terms of the orders tα, log t, (log t)2 and tβ·log t as t → ∞ may occur.
    Zusätzliches Material: 1 Tab.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670180102
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  • 70
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    Digitale Medien
    Masthead (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995) 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670180201
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    Non-orthogonal expansions on the sphere (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 83-120 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Discrete families of functions with the property that every function in a certain space can be represented by its formal Fourier series expansion are developed on the sphere. A Fourier-series-type expansion is obviously true if the family is an orthonormal basis of a Hilbert space, but it also can hold in situations where the family is not orthogonal and is ‘overcomplete’. Furthermore, all functions in our approach are axisymmetric (depending only on the spherical distance) so that they can be used adequately in (rotation) invariant pseudo-differential equations on the sphere. The three classes of examples particularly studied here are (i) Abel-Poisson frames (ii) Gauss-Weierstrass frames and (iii) frames consisting of locally supported kernel functions. Abel-Poisson frames form families of harmonic functions and provide us with powerful approximation tools in potential theory. Gauss-Weierstrass frames are intimately related to the diffusion equation on the sphere and play an important role in multiscale descriptions of image processing on the sphere. The third class enables us to discuss spherical ‘Fourier expansions’ by means of ‘axisymmetric finite elements’.
    Zusätzliches Material: 4 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670180202
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  • 72
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    Local existence of solutions of impedance initial-boundary value problem for non-linear Maxwell equations (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 169-199 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Local existence of solutions of a mixed problem for non-linear Maxwell equations is proved. The solution is so regular that its third derivatives are from L2. However, the considered problem is characteristic we were able to obtain necessary estimate because compatibility conditions were used.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670180302
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  • 73
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    Inverse scattering from an open arc (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 267-293 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A Newton method is presented for the approximate solution of the inverse problem to determine the shape of a sound-soft or perfectly conducting arc from a knowledge of the far-field pattern for the scattering of time-harmonic plane waves. Fréchet differentiability with respect to the boundary is shown for the far-field operator, which for a fixed incident wave maps the boundary arc onto the far-field pattern of the scattered wave. For the sake of completeness, the first part of the paper gives a short outline on the corresponding direct problem via an integral equation method including the numerical solution.
    Zusätzliches Material: 3 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670180403
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  • 74
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    Global solutions for operator Riccati equations with unbounded coefficients: A non-linear semigroup approach (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 317-336 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Let X be a Banach space of real-valued functions on [0, 1] and let ℒ(X) be the space of bounded linear operators on X. We are interested in solutions R:(0, ∞) → ℒ(X) for the operator Riccati equation \documentclass{article}\pagestyle{empty}\begin{document}$$ R′ + TR + RT = TB_1 (t) + TB_2 (t)R + RTB_3 (t) + RTB_4 (t)R, $$\end{document} where T is an unbounded multiplication operator in X and the Bi(t)'s are bounded linear integral operators on X. This equation arises in transport theory as the result of an invariant embedding of the Boltzmann equation. Solutions which are of physical interest are those that take on values in the space of bounded linear operators on L1(0, 1). Conditions on X, R(0), T, and the coefficients are found such that the theory of non-linear semigroups may be used to prove global existence of strong solutions in ℒ(X) that also satisfy R(t) ∊ ℒ(L1(0,1)) for all t ≥ 0.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670180406
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  • 75
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    Masthead (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995) 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670180601
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  • 76
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    Remark on a trace theorem for transmission problems (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 413-421 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper we discuss elliptic transmission problems of second order in plane non-smooth domains with non-homogeneous boundary data. It is known that if the boundary data are homogeneous, then the variational solution of the transmission problem admits a representation as a sum of a regular function and certain singular functions, analogous to that encountered in boundary value problems on corner domains. We determine for which domains arbitrary non-homogeneous boundary data can be reduced to the homogeneous ones preserving availability of the representation formula. In the remaining cases we find the compatibility conditions for the data which also yield such a reduction.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670180506
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  • 77
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    Averaging in non-linear advective transport problems (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 437-448 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Advective transport in a tidal basin is modelled by a non-linear parabolic equation with initial-boundary values. The model includes small effects such as diffusion, the reststream, reaction effects and sources. For a given periodic flow field, the long-time behaviour of the solutions is approximated by using the averaging method. We show the existence of a periodic solution and we demonstrate the asymptotic validity of the approximations for all time using maximum principles.
    Zusätzliches Material: 3 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670180603
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  • 78
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    A generalization of the H-theorem to steady non-equilibrium states. Part 1: A basic decomposition and the linear case (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 507-513 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A generalized relative entropy functional is associated to the evolution of gas in a container with (generally) non-uniform boundary data. A decomposition for its rate in ‘bulk’ and in ‘boundary’ terms is given; for the linear case both have a definite sign. The relation with the strong L1 stability is pointed out.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670180702
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  • 79
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    Stability of semilinear ill-posed problems with a prescribed energy bound (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 549-569 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In the present paper we discuss the stability of semilinear problems of the form Aαu + Gα(u) = ƒ under assumption of an a priori bound for an energy functional Eα(u) ≤ E, where α is a parameter in a metric space M. Following [11] the problem Aαu + Gα(u) = ƒ, Eα(u) ≤ E is called stable in a Hilbert space H at a point α ∊ M if for any ƒ∊H, E, ∊ 〉 0 there exists δ 〉 0 such that for any functions uα1, uα2 satisfying Aαjuαj + Gαj(uαj) = ƒαj, Eαj(uαj) ≤ E, j = 1,2 we have ‖uα1 - uα2H ≤ ∊ provided ρM(αj, α) ≤ δ, ‖ƒαj - ƒ‖H ≤ δ, j = 1,2. In the present paper we obtain stability conditions for the problem Aαu + Gα(u) = ƒ, Eα(u) ≤ E.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670180705
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  • 80
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    Convergence of alternating domain decomposition schemes for kinetic and aerodynamic equations (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 649-670 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A domain decomposition scheme linking linearized kinetic and aerodynamic equations is considered. Convergence of the alternating scheme is shown. Moreover the physical correctness of the obtained coupled solutions is discussed.
    Zusätzliches Material: 4 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670180806
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    Masthead (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995) 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670180901
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  • 82
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    Quaternionic representation of the 3D elastic and thermoelastic boundary problems (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 697-708 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: This paper contains new representations of the 3D elasticity and thermoelasticity problems, expressed in terms of regular quaternion functions, which in 3D and 4D have properties analogous to those of complex analytical functions in 2D. The known and some new results, described in the paper, are used to formulate boundary 3D problems, related to the theory. The formulae obtained are very similar to those given by Muskhelishvili for 2D boundary problems. The obtained representations can be used for development of a 3D boundary element method in numerical analysis.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670180904
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  • 83
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    Calculation of microstrains and microstresses in a thick non-symmetric heterogeneous plate by homogenization (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 723-737 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We consider the thermoelastic behaviour of a thick heterogeneous plate containing in its thickness a large number of periodically distributed transverse holes or inclusions. We use the Reissner-Mindlin thermoelastic linear model of thick plates with a known temperature and we distinguish displacements in the upper and lower part of the plate with respect to the middle plane. Due to the structure of the plate, thermal and elastic coefficients are non-uniformly and rapidly oscillating functions of the space variable. Two-scale convergence, which is the state of the art in mathematical homogenization technics, is used and gives convergence results and formulae allowing to calculate the distribution of microstrains and microstresses inside the plate when a macroscopic behaviour is given.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670180906
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  • 84
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    Global wellposedness for quasi-linear symmetric hyperbolic systems with regularized coefficients (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 773-787 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Following the abstract setting of [8] and using the global results of [2], global wellposedness and regularity results are proved for the solutions of quasi-linear symmetric hyperbolic systems with bounded coefficients which are regularized by a convolution in the space variables with a regularizing function. In the case of unbounded regularized coefficients, local existence of classical solutions is proved, as well as uniqueness and regularity of (not necessarily existing) global weak solutions with initial value in a Sobolev space. As the regularizing function tends to Dirac's δ, local-in-time convergence to the classical solution of the non-regularized problem is proved.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670181003
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  • 85
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    Masthead (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995) 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670181101
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  • 86
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    Masthead (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995) 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670181201
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  • 87
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    On the stationary quasi-Newtonian flow obeying a power-law (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 927-948 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We investigate in this paper existence of a weak solution for a stationary incompressible Navier-Stokes system with non-linear viscosity and with non-homogeneous boundary conditions for velocity on the boundary. Our concern is with the viscosity obeying the power-law dependence ν(ξ) = ∣Tr(ξξ*)∣r/2-1, r 〈 2, on shear stress ξ. It is corresponding to most quasi-Newtonian flows with injection on the boundary. Since for r ≤ 2 the inertial term precludes any a priori estimate in general, we suppose the Reynolds number is not too large. Using the specific algebraic structure of the Navier-Stokes system we prove existence of at least one approximate solution. The constructed approximate solution turns out to be uniformly bounded in W1,r (Omega;)n and using monotonicity and compactness we successfully pass to the limit for r ≥ 3n/(n + 2). For 3n/(n + 2) 〉 r 〉 2n/(n + 2) our construction gives existence of at least one very weak solution. Furthermore, for r ≥ 3n/(n + 2) we prove that all weak solutions lying in the ball in W01,r of radius smaller than critical are equal. Finally, we obtain an existence result for the flow through a thin slab.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670181202
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    On some second-order non-linear systems of a hyperbolic-parabolic type (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 949-957 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We consider local solutions to the Cauchy problem for a class of non-linear hyperbolic-parabolic systems generalizing the systems of elasticity and thermoelasticity. Our main purpose is to relax the usual regularity requirements to include the nonclassical solutions into considerations.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670181203
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    Masthead (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995) 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670181301
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  • 90
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    The free streaming operator: A mathematical model for diffusive multiplying boundary conditions (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 1165-1180 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We show that the free streaming operator with diffusive multiplying boundary conditions is the generator of a quasi-bounded semigroup. We also examine some spectral properties of such an operator.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670181404
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  • 91
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    Masthead (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995) 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670180301
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  • 92
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    Physical model, theoretical aspects and applications of the flight of a ball in the atmosphere. Part III: Theory in the case of vertical angular frequency and in the general spin-case (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 201-223 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: If a ball is viewed as a rigid body, its flight in the atmosphere can be described by six ordinary differential equations, which has been derived in the first part of this paper.In this following third part, some further theoretical aspects in the case of vertical angular frequency will be pointed out using an unknown transformation of the original independent variable, i.e. the time, as indicated in Part II.Last, but not least, the general case of angular frequency is to be treated. A rough qualitative discussion of the solutions is given as well as - if the equations are viewed as a three-dimensional dynamical system - the unique stable equilibrium, which depends on the spin. This equilibrium turns out to be globally attractive, which can be proved by the construction of a suitable Ljapunov function. Then, the ball flight system can be transformed into a fourth-order scalar differential equation.
    Zusätzliches Material: 3 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670180303
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  • 93
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    Linear symmetric hyperbolic systems with characteristic boundary (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 855-870 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The author studies the mixed problem for the linear symmetric hyperbolic systems with maximally non-negative and characteristic boundary condition. Existence of a unique solution is proved inside a suitable class of functions of weighted Sobolev type which takes account of the loss of regularity in the normal direction to the characteristic boundary.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670181103
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  • 94
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    Non-classical interface problems for piecewise homogeneous anisotropic elastic bodies (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 27-49 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Two non-classical model interface problems for piecewise homogeneous anisotropic bodies are studied. In both problems on the contact surface jumps of the normal components of displacement and stress vectors are given. In addition, in the first problem (Problem H) the tangent components of the displacement vectors are given from both sides of the contact surface, while in the second one (Problem G) the tangent components of the stress vectors are prescribed on the same surface. The existence and uniqueness theorems are proved by means of the boundary integral equation method, and representations of solutions by single layer potentials are established. In the investigation the general approach of regularization of the first kind of integral equations is worked out for the case of two-dimensional closed smooth manifolds. An equivalent global regularizer operator is constructed explicitly in the form of a singular integro-differential operator.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670180103
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  • 95
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    Connectivity graphs on two-dimensional surfaces and their application in robotics (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 67-82 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The problem of robot motion planning in an environment with obstacles can often be reduced to the study of connectivity of the robot's free configuration space. In turn, space connectivity can be analysed via the corresponding connectivity graph. For two-degree-of-freedom robots, the free configuration space presents a two-dimensional (2D) surface - a compact subspace of a 2D orientable compact manifold. This paper addresses the following abstract problem: given a compact 2D surface bounded by simple closed curves and lying in an orientable 2D manifold (a sphere, a torus, etc.) and given two points in the subspace, suggest a systematic way of defining the connectivity graph in the subspace, based on its topological properties. The use of space topology results in powerful, from the robotics standpoint, provable algorithms capable of on-line motion planning in an environment with unknown obstacles of arbitrary shapes. This makes the method distinct from other techniques, which require complete information, algebraic representation of space geometry, and off-line computation.
    Zusätzliches Material: 13 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670180105
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  • 96
    Digitale Medien
    Digitale Medien
    On a kinetic model for shallow water waves (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 709-722 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The system of shallow water waves is one of the classical examples for non-linear, two-dimensional conservation laws. The paper investigates a simple kinetic equation depending on a parameter ∊ which leads for ∊ → 0 to the system of shallow water waves. The corresponding ‘equilibrium’ distribution function has a compact support which depends on the eigenvalues of the hyperbolic system. It is shown that this kind of kinetic approach is restricted to a special class of non-linear conservation laws. The kinetic model is used to develop a simple particle method for the numerical solution of shallow water waves. The particle method can be implemented in a straightforward way and produces in test examples sufficiently accurate results.
    Zusätzliches Material: 5 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670180905
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  • 97
    Digitale Medien
    Digitale Medien
    The problem of primary frost heave with frost penetration (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 995-1011 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: This paper is concerned with a mathematical model for the phenomenon of primary frost heave with frost penetration, which appears in the freezing process of wet soil. The problem is formulated in the form of a free boundary problem with two free boundaries. It is shown that there exists a unique classical solution for this problem.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670181205
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  • 98
    Digitale Medien
    Digitale Medien
    Weak solutions to a non-linear hyperbolic system arising in the theory of dielectric liquids (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 1041-1052 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We consider a model of the motion of a viscous dielectric liquid subjected to a DC electric field in the case when the bulk conduction results from the presence of a dissociation-recombination process. The effects of both magnetic field and ionic diffusion are neglected. The existence of at least one weak solution is proved via the method of renormalized solutions.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670181303
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  • 99
    Digitale Medien
    Digitale Medien
    Masthead (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995) 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670181401
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  • 100
    Digitale Medien
    Digitale Medien
    Masthead (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995) 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670181501
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