Numerical viscosity and the entropy condition for conservative difference schemes

Author:
Eitan Tadmor

Journal:
Math. Comp. **43** (1984), 369-381

MSC:
Primary 65M05; Secondary 35L65

MathSciNet review:
758189

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Abstract: Consider a scalar, nonlinear conservative difference scheme satisfying the entropy condition. It is shown that difference schemes containing *more* numerical viscosity will necessarily converge to the unique, physically relevant weak solution of the approximated conservative equation. In particular, entropy satisfying convergence follows for *E* schemes--those containing more numerical viscosity than Godunov's scheme.

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DOI:
https://doi.org/10.1090/S0025-5718-1984-0758189-X

Article copyright:
© Copyright 1984
American Mathematical Society