Numerical viscosity and the entropy condition for conservative difference schemes

Tadmor, Eitan

doi:10.1090/S0025-5718-1984-0758189-X

Numerical viscosity and the entropy condition for conservative difference schemes
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Math. Comp. 43 (1984), 369-381 Request permission

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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