An L1--Error Bound for a Semi-Implicit Difference Scheme Applied to a Stiff System of Conservation Laws

Abstract

A straightforward semi-implicit finite-difference method approximating a system of conservation laws including a stiff relaxation term is analyzed. We show that the error, measured in $\Lone$, is bounded by $O(\sqrt{\dt})$ independent of the stiffness, where the time step $\dt$ represents the mesh size. As a simple corollary we obtain that solutions of the stiff system converge toward the solution of an equilibrium model at a rate of $O(\delta^{1/3})$ in $\Lone$ as the relaxation time $\delta$ tends to zero.