BV estimates of Lax-Friedrichs' scheme for a class of nonlinear hyperbolic conservation laws

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Detail(s)

Original languageEnglish
Pages (from-to)1257-1266
Journal / PublicationProceedings of the American Mathematical Society
Volume131
Issue number4
Publication statusPublished - Apr 2003

Abstract

We give uniform BV estimates and L1-stability of Lax-Friedrichs' scheme for a class of n × n systems of strictly hyperbolic conservation laws whose integral curves of the eigenvector fields are straight lines, i.e., Temple class, under the assumption of small total variation. This implies that the approximate solutions generated via the Lax-Friedrichs' scheme converge to the solution given by the method of vanishing viscosity or the Godunov scheme, and then the Glimm scheme or the wave front tracking method.

Research Area(s)

  • BV estimates, Hyperbolic systems of conservation laws, Lax-Friedrichs' scheme