Communications in Mathematical Sciences

Volume 17 (2019)

Number 6

Convergence rate of an asymptotic preserving scheme for the diffusive limit of the $P$-system with damping

Pages: 1459 – 1486

DOI: https://dx.doi.org/10.4310/CMS.2019.v17.n6.a1

Authors

Solène Bulteau (Laboratoire de Mathématiques Jean Leray, Université de Nantes, CNRS UMR, Nantes, France)

Christophe Berthon (Laboratoire de Mathématiques Jean Leray, Université de Nantes, CNRS UMR, Nantes, France)

Marianne Bessemoulin-Chatard (Laboratoire de Mathématiques Jean Leray, Université de Nantes, CNRS UMR, Nantes, France)

Abstract

This paper aims to establish the convergence rate of approximate solutions of the psystem with damping towards its diffusive limit. We consider an approximation obtained with a full discrete asymptotic preserving finite volume scheme. We study the discrete diffusive limit and establish an exact formulation of the convergence rate. To access such an issue, we estimate the error between approximate solutions of the hyperbolic system and the approximate diffusive limit using a discrete version of the relative entropy method.

Keywords

asymptotic preserving scheme, numerical convergence rate, relative entropy

2010 Mathematics Subject Classification

65M08, 65M12

Full Text (PDF format)

The authors are supported by the MoHyCon project (ANR-17-CE40-0027-01) and the Centre Henri Lebesgue (ANR-11-LABX-0020-01).

Received 8 December 2017

Accepted 11 October 2018

Published 26 December 2019