Abstract: In a previous work by the author, convergence was established for a simple difference scheme approximating a scalar conservation law where the flux was concave, and had a discontinuous spatially varying coefficient. The main result of this paper is an extension of that convergence theorem to the situation where the flux may have any finite number of critical points. As in the previous paper, compactness is established by bounding the total variation of a Temple functional, but the method of achieving this bound, via discrete entropy inequalities, is new.
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