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Mathematics of Computation

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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