Type: Article
Publication Date: 2003-12-22
Citations: 37
DOI: https://doi.org/10.1090/s0025-5718-03-01625-9
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.