Preprint 1996-019
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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