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A relaxation scheme for conservation laws with a discontinuous coefficient


Authors: K. H. Karlsen, C. Klingenberg and N. H. Risebro
Translated by:
Journal: Math. Comp. 73 (2004), 1235-1259
MSC (2000): Primary 35L65, 35L45, 65M06, 65M12
DOI: https://doi.org/10.1090/S0025-5718-03-01625-9
Published electronically: December 22, 2003
MathSciNet review: 2047086
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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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Additional Information

K. H. Karlsen
Affiliation: Department of Mathematics, University of Bergen, Johs. Brunsgt. 12, N-5008 Bergen, Norway
Email: kennethk@mi.uib.no

C. Klingenberg
Affiliation: University of Würzburg, Department of Applied Mathematics and Statistics, Am Hubland, D-97074 Würzburg, Germany
Email: klingen@mathematik.uni-wuerzburg.de

N. H. Risebro
Affiliation: Department of Mathematics, University of Oslo, P. O. Box 1053, Blindern, N-0316 Oslo, Norway
Email: nilshr@math.uio.no

DOI: https://doi.org/10.1090/S0025-5718-03-01625-9
Keywords: Conservation law, discontinuous coefficient, relaxation scheme, convergence compensated compactness, numerical example
Received by editor(s): June 5, 2002
Published electronically: December 22, 2003
Additional Notes: This work has been supported by the BeMatA program of the Research Council of Norway
Article copyright: © Copyright 2003 American Mathematical Society

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