On the convergence of difference approximations to scalar conservation laws
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 by Stanley Osher and Eitan Tadmor PDF
 Math. Comp. 50 (1988), 1951 Request permission
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.References

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Additional Information
 © Copyright 1988 American Mathematical Society
 Journal: Math. Comp. 50 (1988), 1951
 MSC: Primary 65M10; Secondary 35L65, 65M05
 DOI: https://doi.org/10.1090/S0025571819880917817X
 MathSciNet review: 917817