Relative entropy method for the diffusive limit of numerical schemes

par Christophe Berthon (Univ. de Nantes)

mardi 17 janv. 2017, 14:00 → 15:00 Europe/Paris

4e étage, salle 435 (UMPA, ENS Lyon - Site Monod)

This work 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.