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NUMERICAL CONVERGENCE RATE FOR A DIFFUSIVE LIMIT OF HYPERBOLIC SYSTEMS: p-SYSTEM WITH DAMPING

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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https://hal.archives-ouvertes.fr/hal-01360107
Contributor : Marianne Bessemoulin-Chatard <>
Submitted on : Monday, September 5, 2016 - 1:52:20 PM
Last modification on : Tuesday, December 8, 2020 - 9:48:04 AM
Long-term archiving on: : Tuesday, December 6, 2016 - 1:02:14 PM

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  • HAL Id : hal-01360107, version 1
  • ARXIV : 1609.01436

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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, Société de Mathématiques Appliquées et Industrielles (SMAI), 2016. ⟨hal-01360107⟩

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