Preprint 2002-034

A Relaxation Scheme for Conservation Laws with a Discontinuous Coefficient

Abstract: 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.

Paper:
Available as PDF (1.7 Mbytes).
Author(s):
Kenneth H. Karlsen, <kennethk@mi.uib.no>
Christian Klingenberg , <christian.klingenberg@iwr.uni-heidelberg.de>
Nils Henrik Risebro, <nilshr@math.uio.no>
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