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This paper deals with diffusive limit of the -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 -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.
DOI : 10.5802/smai-jcm.10
Keywords: Asymptotic Preserving scheme, numerical convergence rate, relative entropy
Berthon, Christophe 1 ; Bessemoulin-Chatard, Marianne 1 ; Mathis, Hélène 1
@article{SMAI-JCM_2016__2__99_0,
author = {Berthon, Christophe and Bessemoulin-Chatard, Marianne and Mathis, H\'el\`ene},
title = {Numerical convergence rate for a diffusive limit of hyperbolic systems: $p$-system with damping},
journal = {The SMAI Journal of computational mathematics},
pages = {99--119},
publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
volume = {2},
year = {2016},
doi = {10.5802/smai-jcm.10},
mrnumber = {3633546},
zbl = {1416.65289},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.5802/smai-jcm.10/}
}
TY - JOUR AU - Berthon, Christophe AU - Bessemoulin-Chatard, Marianne AU - Mathis, Hélène TI - Numerical convergence rate for a diffusive limit of hyperbolic systems: $p$-system with damping JO - The SMAI Journal of computational mathematics PY - 2016 SP - 99 EP - 119 VL - 2 PB - Société de Mathématiques Appliquées et Industrielles UR - http://geodesic.mathdoc.fr/articles/10.5802/smai-jcm.10/ DO - 10.5802/smai-jcm.10 LA - en ID - SMAI-JCM_2016__2__99_0 ER -
%0 Journal Article %A Berthon, Christophe %A Bessemoulin-Chatard, Marianne %A Mathis, Hélène %T Numerical convergence rate for a diffusive limit of hyperbolic systems: $p$-system with damping %J The SMAI Journal of computational mathematics %D 2016 %P 99-119 %V 2 %I Société de Mathématiques Appliquées et Industrielles %U http://geodesic.mathdoc.fr/articles/10.5802/smai-jcm.10/ %R 10.5802/smai-jcm.10 %G en %F SMAI-JCM_2016__2__99_0
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
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