Numerical convergence rate for a diffusive limit of hyperbolic systems: $p$-system with damping
The SMAI journal of computational mathematics, Volume 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.

Published online:
DOI: https://doi.org/10.5802/smai-jcm.10
Classification: 65M08,  65M12
Keywords: Asymptotic Preserving scheme, numerical convergence rate, relative entropy
@article{SMAI-JCM_2016__2__99_0,
author = {Christophe Berthon and Marianne Bessemoulin-Chatard and H\'el\ene Mathis},
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 = {https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.10/}
}
Christophe Berthon; Marianne Bessemoulin-Chatard; Hélène Mathis. Numerical convergence rate for a diffusive limit of hyperbolic systems: $p$-system with damping. The SMAI journal of computational mathematics, Volume 2 (2016) , pp. 99-119. doi : 10.5802/smai-jcm.10. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.10/`

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