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

International audienceThis paper aims to establish the convergence rate of approximate solutions of the p-system 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