Maximal entropy dissipation numerical scheme for conservation law systems

Abstract

This paper presents a numerical finite volume method for conservation law systems that are adapted to the principle of maximal dissipation. The general assumptions are the existence of a strictly convex entropy functional and the finite propagation speed property of a given system. The procedure is based on a numerical flux construction obtained by the minimization of the entropy functional in each time step. The scheme satisfies assumptions of the Lax-Wendroff theorem. A limiting solution obtained by this scheme is compared with the classical weak solutions obtained by the Glimm or the Wave Front Tracking algorithm for one-dimensional systems.