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This paper deals with diffusive limit of the p-system with damping and itsapproximation by an Asymptotic Preserving (AP) Finite Volume scheme. Providedthe system is endowed with an entropy-entropy flux pair, we give theconvergence rate of classical solutions of the p-system with damping towardsthe smooth solutions of the porous media equation using a relative entropymethod. Adopting a semi-discrete scheme, we establish that the convergence rateis preserved by the approximated solutions. Several numerical experimentsillustrate the relevance of this result.

Numerical Convergence Rate for a Diffusive Limit of Hyperbolic Systems: p-System with Damping