A relaxation scheme for conservation laws with a discontinuous coefficient

Karlsen, K.; Klingenberg, C.; Risebro, N.

doi:10.1090/S0025-5718-03-01625-9

A relaxation scheme for conservation laws with a discontinuous coefficient
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by K. H. Karlsen, C. Klingenberg and N. H. Risebro PDF

Math. Comp. 73 (2004), 1235-1259 Request permission

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.

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