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

Abstract

We give uniform BV estimates and L 1 L^1 -stability of Lax-Friedrichs’ scheme for a class of n × n n\times 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.