Tadmor, Eitan Numerical viscosity and the entropy condition for conservative difference schemes. (English) Zbl 0587.65058 Math. Comput. 43, 369-381 (1984). 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 Cited in 1 ReviewCited in 83 Documents MSC: 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 35L65 Hyperbolic conservation laws Keywords:Godunov scheme; Lax-Friedrichs scheme; entropy; convergence; numerical viscosity PDFBibTeX XMLCite \textit{E. Tadmor}, Math. Comput. 43, 369--381 (1984; Zbl 0587.65058) Full Text: DOI