A 2ND-ORDER ENTROPY SATISFYING SCHEME FOR SYSTEMS OF CONSERVATION-LAWS

In this work, we are concerned with the construction of second order n umerical schemes for hyperbolic systems of conservation law. We sugges t to use the fact that, for systems, the mathematical entropy is a dec reasing function of time, rather than the classical total variation de creasing property, which is mostly satisfied by scalar equations. We d efine an entropy satisfying a version of van Leer's MUSCL scheme, whic h introduces a nonlinear coupling between the characteristic variables of the system. We prove a result of strong convergence for the scheme , which extends to systems a recent approach proposed by Bouchut, Boud arias, and Perthame [2].