Preprint 1996-019

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

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 , mailto:wens@ifi.uio.no

Aslak Tveito , mailto:aslak@ifi.uio.no

Ragnar Winther, mailto:ragnar@ifi.uio.no

Publishing information:

Preprint 1995-5, Department for Informatics, University of Oslo, Norway. Accepted for publication by BIT.

Submitted by:

mailto:wens@ifi.uio.no August 2 1996.