### A system of conservation laws including a stiff relaxation term; the 2D case

Wen Shen, Aslak Tveito, and Ragnar Winther

Abstract: We analyze a system of conservation laws in two space dimensions with stiff relaxation terms. A semi-implicit finite difference method approximating the system is studied and an error bound of order $\cal{O}(\sqrt{\dt})$ measured in $L^1$ is derived. This error bound is independent of the relaxation time $\delta>0$. Furthermore, it is proved that the solutions of the system converge towards the solutions of the equilibrium model as the relaxation time $\delta$ tends to zero, and that the rate of convergence measured in $L^1$ is of order $\cal{O}(\delta^{1/3})$. Finally, we present some numerical illustrations.

Paper:
Available as PostScript
Title:
A system of conservation laws including a stiff relaxation term; the 2D case
Author(s):
Wen Shen , <wens@ifi.uio.no>
Aslak Tveito , <aslak@ifi.uio.no>
Ragnar Winther, <ragnar@ifi.uio.no>
Publishing information:
Preprint 1995-5, Department for Informatics, University of Oslo, Norway. Accepted for publication by BIT.
Submitted by:
<wens@ifi.uio.no> August 2 1996.

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