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  • 1
    Electronic Resource
    Electronic Resource
    A system of conservation laws including a stiff relaxation term; the 2D case (1996)
    Springer
    BIT 36 (1996), S. 786-813 
    Details
    ISSN: 1572-9125
    Keywords: Hyperbolic conservation laws ; two space dimensions ; relaxation terms ; non-equilibrium ; error estimate ; rate of convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We analyze a system of conservation laws in two space dimensions with a stiff relaxation term. A semi-implicit finite difference method approximating the system is studied and an error bound of order $$\mathcal{O}(\sqrt {\Delta t} )$$ measured inL 1 is derived. This error bound is independent of the relaxation time δ 〉 0. Furthermore, it is proved that the solutions of the system converge towards the solution of an equilibrium model as the relaxation time δ tends to zero, and that the rate of convergence measured inL 1 is of order $$\mathcal{O}(\delta ^{1/3} )$$ . Finally, we present some numerical illustrations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01733792
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Multigrid in H (div) and H (curl) (2000)
    Springer
    Numerische Mathematik 85 (2000), S. 197-217 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991):65N55, 65N30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. We consider the solution of systems of linear algebraic equations which arise from the finite element discretization of variational problems posed in the Hilbert spaces ${\bf H (div)}$ and ${\bf H (curl)}$ in three dimensions. We show that if appropriate finite element spaces and appropriate additive or multiplicative Schwarz smoothers are used, then the multigrid V-cycle is an efficient solver and preconditioner for the discrete operator. All results are uniform with respect to the mesh size, the number of mesh levels, and weights on the two terms in the inner products.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00005386
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Instability of Buckley-Leverett flow in a heterogeneous medium (1992)
    Springer
    Transport in porous media 9 (1992), S. 165-185 
    Details
    ISSN: 1573-1634
    Keywords: oil recovery ; instability ; heterogeneous medium ; shock waves
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract We study the simultaneous one-dimensional flow of water and oil in a heterogeneous medium modelled by the Buckley-Leverett equation. It is shown both by analytical solutions and by numerical experiments that this hyperbolic model is unstable in the following sense: Perturbations in physical parameters in a tiny region of the reservoir may lead to a totally different picture of the flow. This means that simulation results obtained by solving the hyperbolic Buckley-Leverett equation may be unreliable.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00611965
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Error estimates for a galerkin approximation of a parabolic control problem (1978)
    Springer
    Annali di matematica pura ed applicata 117 (1978), S. 173-206 
    Details
    ISSN: 1618-1891
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Numerical approximation of a parabolic control problem with a Neumann boundary condition control is considered. The observation is the final state. The numerical approximation is based on backward discretization with respect to time and a Galerkin method in the space variables. Optimal (except for a logarithmic term) L2 error estimates are derived for the optimal state. Certain error estimates for the optimal control are also given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02417890
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Domain embedding preconditioners for mixed systems (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 5 (1998), S. 321-345 
    Details
    ISSN: 1070-5325
    Keywords: second order elliptic problems ; Dirichlet boundary conditions ; mixed finite elements ; preconditioning ; domain embedding ; auxiliary space method ; non-conforming finite elements ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we study block diagonal preconditioners for mixed systems derived from the Dirichlet problems for second order elliptic equations. The main purpose is to discuss how an embedding of the original computational domain into a simpler extended can be utilized in this case. We show that a family of uniform preconditioners for the corresponding problem on the extended, or fictitious, domain leads directly to uniform preconditioners for the original problem. This is in contrast to the situation for the standard finite element method, where the domain embedding approach for the Dirichlet problem is less obvious. Copyright © 1999 John Wiley & Sons, Ltd.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
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  • 6
    Book
    Book
    Introduction to partial differential equations : a computational approach; 29 (1998)
    New York u. a. :Springer,
    Details
    Title: Introduction to partial differential equations : a computational approach; 29
    Author: Tveito, Aslak
    Contributer: Winther, Ragnar
    Publisher: New York u. a. :Springer,
    Year of publication: 1998
    Pages: 392 S.
    Series Statement: Texts in applied mathematics 29
    Type of Medium: Book
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    Zuse Institute Berlin get availability status
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