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Convergence of difference schemes with high resolution for conservation laws

Publication ,  Journal Article
Chen, GQ; Liu, JG
Published in: Mathematics of Computation
January 1, 1997

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 Scholars

Published In

Mathematics of Computation

DOI

ISSN

0025-5718

Publication Date

January 1, 1997

Volume

66

Issue

219

Start / End Page

1027 / 1053

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0802 Computation Theory and Mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
 

Citation

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Chen, G. Q., & Liu, J. G. (1997). Convergence of difference schemes with high resolution for conservation laws. Mathematics of Computation, 66(219), 1027–1053. https://doi.org/10.1090/s0025-5718-97-00859-4
Chen, G. Q., and J. G. Liu. “Convergence of difference schemes with high resolution for conservation laws.” Mathematics of Computation 66, no. 219 (January 1, 1997): 1027–53. https://doi.org/10.1090/s0025-5718-97-00859-4.
Chen GQ, Liu JG. Convergence of difference schemes with high resolution for conservation laws. Mathematics of Computation. 1997 Jan 1;66(219):1027–53.
Chen, G. Q., and J. G. Liu. “Convergence of difference schemes with high resolution for conservation laws.” Mathematics of Computation, vol. 66, no. 219, Jan. 1997, pp. 1027–53. Scopus, doi:10.1090/s0025-5718-97-00859-4.
Chen GQ, Liu JG. Convergence of difference schemes with high resolution for conservation laws. Mathematics of Computation. 1997 Jan 1;66(219):1027–1053.
Journal cover image

Published In

Mathematics of Computation

DOI

ISSN

0025-5718

Publication Date

January 1, 1997

Volume

66

Issue

219

Start / End Page

1027 / 1053

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0802 Computation Theory and Mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics