### An $L^1$-error bound for a semiimplicit difference scheme applied to a stiff system of conservation laws

Hans Joachim Schroll, Aslak Tveito, and Ragnar Winther

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. Furthermore, we show that solutions of the stiff system converge towards the solution of an equilibrium model at a rate of $O(\delta^{1/3})$ in $\Lone$ as the relaxation time $\delta$ tends to zero.

Paper:
Available as PostScript
Title:
An $L^1$-error bound for a semiimplicit difference scheme applied to a stiff system of conservation laws
Author(s):
Hans Joachim Schroll, <schroll@igpm.rwth-aachen.de>
Aslak Tveito , <aslak@ifi.uio.no>
Ragnar Winther, <ragnar@ifi.uio.no>
Publishing information:
To appear in Siam J. Num. An.