Monotone difference approximations for scalar conservation laws

Michael G. Crandall, Andrew Majda

Research output: Contribution to journalArticle

Abstract

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
Volume34
Issue number149
DOIs
StatePublished - 1980

Fingerprint

Monotone Approximation
Monotone Scheme
Difference Approximation
Scalar Conservation Laws
Difference Scheme
Conservation
Converge
Entropy Condition
Stagnation Point
Upwind Scheme
Stability and Convergence
Convergence Properties
Convergence Results
Weak Solution
Entropy
Generalization
Form

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

Cite this

Monotone difference approximations for scalar conservation laws. / Crandall, Michael G.; Majda, Andrew.

In: Mathematics of Computation, Vol. 34, No. 149, 1980, p. 1-21.

Research output: Contribution to journalArticle

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