High Resolution Schemes and the Entropy Condition

摘要: A systematic procedure for constructing semidiscrete, second order accurate, variation diminishing, five-point band width, approximations to scalar conservation laws, is presented. These schemes are constructed also satisfy a single discrete entropy inequality. Thus, in the convex flux case, we prove convergence unique physically correct solution. For hyperbolic systems of formally use this construction extend first author’s accurate scheme, and show (under some minor technical hypotheses) that limit solutions an Results concerning shocks, maximum principle, maximal accuracy obtained. Numerical applications