On Entropy Conditions of High Resolution Schemes for Scalar Conservation Laws

Abstract

In this paper a kind of quadratic cell entropy inequalities of second order resolution SOR-TVD schemes is obtained for scalar hyperbolic conservation laws with strictly convex (concave) fluxes, which in turn implies the convergence of the schemes to the physically relevant solution of the problem. The theoretical results obtained in this paper improve the main results of Osher and Tadmor [6].