Convergence of Difference Schemes with Highresolution for Conservation
نویسنده
چکیده
We are concerned with the convergence of Lax-Wendroo type schemes with high resolution to the entropy solutions for conservation laws. These schemes include the original Lax-Wendroo scheme proposed by Lax and Wendroo in 1960 and its two step versions{the Richtmyer scheme and the MacCormack scheme. For the convex scalar conservation laws with algebraic growth ux functions, we prove the convergence of these schemes to the weak solutions satisfying appropriate entropy inequalities. The proof is based on detailed L p estimates of the approximate solutions, H ?1 compactness estimates of the corresponding entropy dissipation measures, and some compensated compactness frameworks. Then these techniques are generalized to study the convergence problem for the nonconvex scalar case and the hyperbolic systems of conservation laws.
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