A Difference Scheme for Conservation Laws with a Discontinuous Flux: The Nonconvex Case

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 [J. D. Towers, SIAM J. Numer. Anal., 38 (2000), pp. 681--698]. 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. Additionally, spatially varying source terms are allowed. The spatially varying numerical flux is also shown to satisfy maximum and minimum principles and to be total variation decreasing (TVD) in time.