A relaxation scheme for conservation laws with a discontinuous coefficient

Type: Article

Publication Date: 2003-12-22

Citations: 37

DOI: https://doi.org/10.1090/s0025-5718-03-01625-9

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.

Locations

  • Mathematics of Computation - View - PDF
  • CiteSeer X (The Pennsylvania State University) - View - PDF

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