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Christophe Berthon; Marianne Bessemoulin-Chatard; Hélène Mathis
Numerical convergence rate for a diffusive limit of hyperbolic systems: $p$-system with damping
SMAI-Journal of computational mathematics, 2 (2016), p. 99-119, doi: 10.5802/smai-jcm.10
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Class. Math.: 65M08, 65M12
Keywords: Asymptotic Preserving scheme, numerical convergence rate, relative entropy

Abstract

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.

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