Title :

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

Author(s) :

Cancès, Clément [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
Mathis, Hélène [Auteur]
Laboratoire de Mathématiques Jean Leray [LMJL]
Seguin, Nicolas [Auteur]
Laboratoire de Mathématiques Jean Leray [LMJL]

Journal title :

SIAM Journal on Numerical Analysis

Pages :

1263-1287

Publisher :

Society for Industrial and Applied Mathematics

Publication date :

2016

ISSN :

0036-1429

English keyword(s) :

error estimates
finite volume schemes
relative entropy
hyperbolic systems
strong solutions

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Analyse numérique [math.NA]

English abstract : [en]

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 ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL