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  • 1
    Electronic Resource
    Electronic Resource
    A Galerkin method with modified piecewise polynomials for solving a second-order boundary value problem (1976)
    Springer
    Numerische Mathematik 27 (1976), S. 11-20 
    Details
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The classical Ritz-Galerkin method is applied to a linear, second-order, self-adjoint boundary value problem. The coefficient functions of the operator exhibit a piecewise smooth behaviour characteristic of some “physical” situations. A trial function is constructed using a modified quintic smooth Hermite space $$\tilde H_0^{(3)} (\pi )$$ , in order to meet some desired regularity conditions for the approximate solution. A collocation technique is used to reduce the amount of computational work. Known convergence properties for the projection method are recalled which, in this particular case, are illustrated by a series of numerical experiments.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01399081
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  • 2
    Electronic Resource
    Electronic Resource
    A finite element model for plasma simulation in multipoles (1979)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 1449-1460 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical model is proposed to simulate the space-time behaviour of a low-density plasma in a linear multipole. Semi-discrete Galerkin techniques are used in conjunction with triangular finite elements. For both space and time discretizations, special techniques are developed to numerically separate the effect of rapid diffusion along the field lines from the slow perpendicular diffusion. Numerical results are exhibited to show how these techniques succeed in eliminating the problems caused by the strong anisotropy of the diffusion coefficient in the strongly curved and very inhomogeneous multipole configuration.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620141003
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    On the relationship between nodal schemes and mixed-hybrid finite elements (1993)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 9 (1993), S. 411-430 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The relationships between a general family of nodal schemes [J.P. Hennart, SIAM J. Sci. Stat. Comput. 3, 264 (1986)] and primal nonconforming as well as mixed-hybrid finite element formulations are explored in this paper. It is shown in particular that the nodal schemes proposed are quite natural extensions in rectangular geometry of the Raviart-Thomas-Nédélec mixed-hybrid finite elements. This paper is a revised and extended version with new numerical results of part of a previous research report [J.P. Hennart, Rapports de Recherche INRIA Vol. 386 (1985)]. © 1993 John Wiley & Sons, Inc.
    Additional Material: 8 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690090406
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    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
    Keywords: mesh-centered finite differences ; nodal methods ; elliptic problems ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 5
    Electronic Resource
    Electronic Resource
    On the numerical analysis of analytical nodal methods (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 4 (1988), S. 233-254 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This article presents the basic numerical analysis of the analytical nodal methods, which were originally developed in the late 1970s in relation with static and dynamic nuclear reactor calculations but are actually applicable to the numerical solution of partial differential equations (PDEs) in general, over fairly regular domains. The basic idea consists in “transverse integrating” the original PDE over all the variables minus one, leading to sets of 1D equations which are then solved in an “analytical” way, using fundamentals as well as particular solutions of the corresponding 1D operators. After examining the existing analytical methods in a critical way, we propose a more satisfactory extended analytical formalism. Superconvergence results finally lead us to useful conclusions with respect to the choice of a particular scheme.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690040306
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