Monotone difference approximations for scalar conservation laws
Authors:
Michael G. Crandall and Andrew Majda
Journal:
Math. Comp. 34 (1980), 121
MSC:
Primary 65M05
MathSciNet review:
551288
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Abstract: A complete selfcontained treatment of the stability and convergence properties of conservationform, 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, Godunov's scheme, the upwind scheme (differenced through stagnation points), and the LaxFriedrichs scheme together with appropriate multidimensional generalizations.
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 G. STRANG, "On the construction and comparison of difference schemes," SIAM J. Numer. Anal., v. 15, 1968, pp. 506517. MR 0235754 (38:4057)
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 A. I. VOL'PERT, "The spaces BV and quasilinear equations," Math. USSR Sb., v. 2, 1967, pp. 225267. MR 0216338 (35:7172)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198005512883
PII:
S 00255718(1980)05512883
Keywords:
Conservation laws,
shock waves difference approximations,
entropy conditions
Article copyright:
© Copyright 1980 American Mathematical Society
