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A relaxation scheme for conservation laws with a discontinuous coefficient |
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| Authors: | K. H. Karlsen C. Klingenberg N. H. Risebro. |
| Affiliation: | Department of Mathematics, University of Bergen, Johs. Brunsgt. 12, N-5008 Bergen, Norway ; University of Würzburg, Department of Applied Mathematics and Statistics, Am Hubland, D-97074 Wü{}rzburg, Germany ; Department of Mathematics, University of Oslo, P. O. Box 1053, Blindern, N-0316 Oslo, Norway |
| 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  . If  , 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  Riemann solver. |
| Keywords: | Conservation law discontinuous coefficient relaxation scheme convergence compensated compactness numerical example |
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