On the convergence of difference approximations to scalar conservation laws
Authors:
Stanley Osher and Eitan Tadmor
Journal:
Math. Comp. 50 (1988), 1951
MSC:
Primary 65M10; Secondary 35L65, 65M05
DOI:
https://doi.org/10.1090/S0025571819880917817X
MathSciNet review:
917817
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Abstract  References  Similar Articles  Additional Information
Abstract: We present a unified treatment of explicit in time, twolevel, secondorder resolution (SOR), totalvariation diminishing (TVD), approximations to scalar conservation laws. The schemes are assumed only to have conservation form and incremental form. We introduce a modified flux and a viscosity coefficient and obtain results in terms of the latter. The existence of a cell entropy inequality is discussed and such an equality for all entropies is shown to imply that the scheme is an E scheme on monotone (actually more general) data, hence at most only firstorder accurate in general. Convergence for TVDSOR schemes approximating convex or concave conservation laws is shown by enforcing a single discrete entropy inequality.

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Article copyright:
© Copyright 1988
American Mathematical Society