A Relaxation Scheme for Conservation Laws with a Discontinuous
We study a relaxation scheme of the Jin and Xin type for conservation laws
with a flux function that depends discontinuously on the spatial location
through a coefficient $k(x)$. If $k\in BV$, we show that the relaxation scheme
produces a sequence of approximate solutions that converge to a weak
solution. The Murat-Tartar compensated compactness method is used to establish
convergence. We present numerical experiments with the relaxation scheme, and
comparisons are made with a front tracking scheme based on an exact $2\times
2$ Riemann solver.
- Available as PDF (1.7 Mbytes).
- Kenneth H. Karlsen,
Christian Klingenberg ,
- Nils Henrik Risebro,
- Publishing information:
- Submitted by:
June 25 2002.
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