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Convergence of difference schemes with high resolutions to conservation laws

Gui-qiang Chen Northwestern University Jian-Guo Liu Temple University

Numerical Analysis and Scientific Computing mathscidoc:1702.25065

MATHEMATICS OF COMPUTATION, 66, (219), 1027{1053, 1997.7
We are concerned with the convergence of Lax-Wendroff type schemes with high resolution to the entropy solutions for conservation laws. These schemes include the original Lax-Wendroff scheme proposed by Lax and Wendroff in 1960 and its two step versions–the Richtmyer 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 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
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@inproceedings{gui-qiang1997convergence,
  title={Convergence of difference schemes with high resolutions to conservation laws},
  author={Gui-qiang Chen, and Jian-Guo Liu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209130500491621398},
  booktitle={MATHEMATICS OF COMPUTATION},
  volume={66},
  number={219},
  pages={1027{1053},
  year={1997},
}
Gui-qiang Chen, and Jian-Guo Liu. Convergence of difference schemes with high resolutions to conservation laws. 1997. Vol. 66. In MATHEMATICS OF COMPUTATION. pp.1027{1053. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209130500491621398.
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