Numerical viscosity and the entropy condition for conservative difference schemes. (English) Zbl 0587.65058

Several difference schemes approximating the following scalar conservation law \[ \partial u/\partial t(x,t)+\partial f/\partial x(u(x,t))=0 \] are examined from the point of view of the entropy condition. The author studies the Godunov scheme, the Lax-Friedrichs scheme and other schemes in general form with viscosity and shows that entropy satisfying convergence follows from the following fact: the difference scheme contains more numerical viscosity than the Godunov scheme.
Reviewer: Gy.Molnárka


65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
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