Communications in Mathematical Sciences
Volume 17 (2019)
Convergence rate of an asymptotic preserving scheme for the diffusive limit of the $P$-system with damping
Pages: 1459 – 1486
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.
asymptotic preserving scheme, numerical convergence rate, relative entropy
2010 Mathematics Subject Classification
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