CONVERGENCE RATE OF GLIMM SCHEME FOR GENERAL SYSTEMS OF HYPERBOLIC CONSERVATION LAWS

Abstract

In this paper, we consider the convergence rate of the deterministic Glimm scheme for general systems of hyperbolic conservation laws without assuming either genuine nonlinearity or linear degeneracy on the characteristic fields. It is shown that the convergence rate is $o(1)s^{\frac{1}{4}}|\ln s|$ compared to $o(1)s^{\frac{1}{2}}|\ln s|$ obtained in [3] for the case when the charateristic field is either genuinely nonlinear or linear degenerate. Here $s$ is the mesh size in the time direction.