Error estimate for the approximation of nonlinear conservation laws on bounded domains by the finite volume method-Reference-Cited by-同舟云学术

Error estimate for the approximation of nonlinear conservation laws on bounded domains by the finite volume method

Published:2005-08-12 Issue:253 Volume:75 Page:113-150
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Ohlberger Mario,Vovelle Julien

Abstract

In this paper we derive a priori and a posteriori error estimates for cell centered finite volume approximations of nonlinear conservation laws on polygonal bounded domains. Numerical experiments show the applicability of the a posteriori result for the derivation of local adaptive solution strategies.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/2006-75-253/S0025-5718-05-01770-9/S0025-5718-05-01770-9.pdf

Reference34 articles.

1. Numerical viscosity and convergence of finite volume methods for conservation laws with boundary conditions;Benharbit, S.;SIAM J. Numer. Anal.,1995

2. First order quasilinear equations with boundary conditions;Bardos, C.;Comm. Partial Differential Equations,1979

3. Entropy solutions for nonlinear degenerate problems;Carrillo, José;Arch. Ration. Mech. Anal.,1999

4. Convergence of the finite volume method for multidimensional conservation laws;Cockburn, B.;SIAM J. Numer. Anal.,1995

5. Convergence of the finite volume method for multidimensional conservation laws;Cockburn, B.;SIAM J. Numer. Anal.,1995

Cited by 16 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. An $$h-$$Adaptive Local Discontinuous Galerkin Method for Simulating Wormhole Propagation with Darcy–Forcheiner Model;Journal of Scientific Computing;2020-02

2. Convergence Rates of Monotone Schemes for Conservation Laws with Discontinuous Flux;SIAM Journal on Numerical Analysis;2020-01

3. Error estimates for a finite difference scheme associated with Hamilton–Jacobi equations on a junction;Numerische Mathematik;2019-05-17

4. A convergent finite difference scheme for the Ostrovsky–Hunter equation with Dirichlet boundary conditions;BIT Numerical Mathematics;2019-03-13

5. Finite Volume Methods: Foundation and Analysis;Encyclopedia of Computational Mechanics Second Edition;2017-12-17