# Error estimate for time-explicit finite volume approximation of strong solutions to systems of conservation laws

1 RAPSODI - Reliable numerical approximations of dissipative systems
LPP - Laboratoire Paul Painlevé - UMR 8524, Inria Lille - Nord Europe
Abstract : We study the finite volume approximation of strong solutions to nonlinear systems of conservation laws. We focus on time-explicit schemes on unstructured meshes, with entropy satisfying numerical fluxes. The numerical entropy dissipation is quantified at each interface of the mesh, which enables to prove a weak–BV estimate for the numerical approximation under a strengthen CFL condition. Then we derive error estimates in the multidimensional case, using the relative entropy between the strong solution and its finite volume approximation. The error terms are carefully studied, leading to a classical $h^1/4$ estimate in $L^2$ under this strengthen CFL condition.
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Article dans une revue
SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2016, 54 (2), pp.1263-1287
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https://hal.archives-ouvertes.fr/hal-00798287
Contributeur : Clément Cancès <>
Soumis le : vendredi 5 février 2016 - 14:27:54
Dernière modification le : jeudi 11 janvier 2018 - 06:27:32

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• HAL Id : hal-00798287, version 3
• ARXIV : 1602.02128

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Clément Cancès, Hélène Mathis, Nicolas Seguin. Error estimate for time-explicit finite volume approximation of strong solutions to systems of conservation laws. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2016, 54 (2), pp.1263-1287. 〈hal-00798287v3〉

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