CONVERGENCE OF GODUNOV-TYPE SCHEMES FOR SCALARCONSERVATION LAWS UNDER LARGE TIME STEPS

摘要

In this paper, we consider convergence of classical high-order Godunov-type schemestowards entropy solutions for scalar conservation laws. It is well known that sufficient conditionsfor such convergence include total variation boundedness of the reconstruction and cell or wavewiseentropy inequalities. We prove that under large time steps, we only need total variation boundednessof the reconstruction to guarantee such convergence. We discuss high-order total variation boundedreconstructions to fulfill this sufficient condition and provide numerical examples on one-dimensionalconvex conservation laws to assess the performance of such large time step Godunov-type meth-ods. To demonstrate the generality of this approach, we also prove convergence and give numericalexamples for a large time step Godunov-like scheme involving Sanders' third-order total variationdiminishing reconstruction using both cell averages and point values at cell boundaries.