Monotone difference approximations for scalar conservation laws

Michael G. Crandall, Andrew Majda

Research output: Contribution to journalArticlepeer-review


A complete self-contained treatment of the stability and convergence properties of conservation-form, monotone difference approximations to scalar conservation laws in several space variables is developed. In particular, the authors prove that general monotone difference schemes always converge and that they converge to the physical weak solution satisfying the entropy condition. Rigorous convergence results follow for dimensional splitting algorithms when each step is approximated by a monotone difference scheme. The results are general enough to include, for instance, Godunovs scheme, the upwind scheme (differenced through stagnation points), and the Lax-Friedrichs scheme together with appropriate multi-dimensional generalizations.

Original languageEnglish (US)
Pages (from-to)1-21
Number of pages21
JournalMathematics of Computation
Issue number149
StatePublished - Jan 1980

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics


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