Monotone difference approximations for scalar conservation laws
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 by Michael G. Crandall and Andrew Majda PDF
 Math. Comp. 34 (1980), 121 Request permission
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.References

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Additional Information
 © Copyright 1980 American Mathematical Society
 Journal: Math. Comp. 34 (1980), 121
 MSC: Primary 65M05
 DOI: https://doi.org/10.1090/S00255718198005512883
 MathSciNet review: 551288