Preprint 1999-024

Convergence of a Difference Scheme for Conservation Laws with a Discontinuous Flux

John Towers

Abstract: Convergence is established for a scalar difference scheme, based on the Godunov or Engquist-Osher flux, for scalar conservation laws having a flux that is spatially dependent through a possibly discontinuous coefficient. Other works in this direction have established convergence for methods employing the solution of 2x2 Riemann problems. The algorithm discussed here uses only scalar Riemann solvers. Satisfaction of a set of Kruzkov-type entropy conditions is established for the limit solution, from which geometric entropy conditions follow. Assuming a piecewise constant coefficient, it is shown that these conditions imply $L^1$-contractiveness for piecewise $C^1$ solutions, thus extending a well known theorem.

Available as PostScript.
John Towers, <>
Publishing information:
Revised version from November 3 1999.
Submitted by:
<> September 18 1999.

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Last modified: Wed Nov 3 11:17:40 1999