Numerical Convergence Rate for a Diffusive Limit of Hyperbolic Systems: p-System with Damping
Numerical Analysis
2016-09-07 v1
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.
Keywords
Cite
@article{arxiv.1609.01436,
title = {Numerical Convergence Rate for a Diffusive Limit of Hyperbolic Systems: p-System with Damping},
author = {Christophe Berthon and Marianne Bessemoulin-Chatard and Hélène Mathis},
journal= {arXiv preprint arXiv:1609.01436},
year = {2016}
}