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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