Convergence of difference schemes with high resolution for conservation laws


Journal Article

We are concerned with the convergence of Lax-Weridroff type schemes with high resolution to the entropy solutions fo: conservation laws. These schemes include the original Lax-Wendroff scheme proposed by Lax and Wendroff in 1960 and its two step versions-the Richtrayer scheme and the MacCormack scheme. For the convex scalar conservation laws with algebraic growth flux functions, we prove the convergence of these schemes to the weak solutions satisfying appropriate entropy inequalities. The proof is based on detailed Lp 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.

Duke Authors

Cited Authors

  • Chen, GQ; Liu, JG

Published Date

  • July 1, 1997

Published In

Volume / Issue

  • 66 / 219

Start / End Page

  • 1027 - 1053

International Standard Serial Number (ISSN)

  • 0025-5718

Citation Source

  • Scopus