Numerical convergence rate for a diffusive limit of hyperbolic systems: p-system with damping
Berthon, Christophe1 ; Bessemoulin-Chatard, Marianne1 ; Mathis, Hélène1
1 Université de Nantes - Laboratoire de Mathématiques Jean Leray, CNRS UMR 6629 - 2 rue de la Houssinière, BP 92208 - 44322 Nantes, France
The SMAI Journal of computational mathematics, Tome 2 (2016), pp. 99-119.

This paper deals with diffusive limit of the p-system with damping and its approximation by an Asymptotic Preserving (AP) Finite Volume scheme. Provided the system is endowed with an entropy-entropy flux pair, we give the convergence rate of classical solutions of the p-system with damping towards the smooth solutions of the porous media equation using a relative entropy method. Adopting a semi-discrete scheme, we establish that the convergence rate is preserved by the approximated solutions. Several numerical experiments illustrate the relevance of this result.

Publié le :
DOI : 10.5802/smai-jcm.10
Classification : 65M08, 65M12
Mots clés : Asymptotic Preserving scheme, numerical convergence rate, relative entropy
Berthon, Christophe 1 ; Bessemoulin-Chatard, Marianne 1 ; Mathis, Hélène 1

1 Université de Nantes - Laboratoire de Mathématiques Jean Leray, CNRS UMR 6629 - 2 rue de la Houssinière, BP 92208 - 44322 Nantes, France 
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     title = {Numerical convergence rate for a diffusive limit of hyperbolic systems: $p$-system with damping},
     journal = {The SMAI Journal of computational mathematics},
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Berthon, Christophe; Bessemoulin-Chatard, Marianne; Mathis, Hélène. Numerical convergence rate for a diffusive limit of hyperbolic systems: $p$-system with damping. The SMAI Journal of computational mathematics, Tome 2 (2016), pp. 99-119. doi : 10.5802/smai-jcm.10. http://archive.numdam.org/articles/10.5802/smai-jcm.10/

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