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

Christophe Berthon (1) , Marianne Bessemoulin-Chatard (1) , Hélène Mathis (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

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.

Mots clés: Asymptotic Preserving scheme; numerical convergence rate; relative entropy

Domaines: Analyse numérique [math.NA]

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, 2016. ⟨hal-01360107⟩