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arXiv · 1609.01436

Numerical Convergence Rate for a Diffusive Limit of Hyperbolic Systems: p-System with Damping

Christophe Berthon·Marianne Bessemoulin-Chatard·Hélène Mathis
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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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Christophe Berthon, Marianne Bessemoulin-Chatard, Hélène Mathis. 2016-09-06. Numerical Convergence Rate for a Diffusive Limit of Hyperbolic Systems: p-System with Damping. https://arxiv.org/abs/1609.01436

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