Numerical Convergence Rate for a Diffusive Limit of Hyperbolic Systems:   p-System with Damping
  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. 
Christophe Berthon (LMJL), Marianne Bessemoulin-Chatard (LMJL),   H\'el\`ene Mathis (LMJL)
math.NA