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

@article{Towers2000ConvergenceOA,
title={Convergence of a Difference Scheme for Conservation Laws with a Discontinuous Flux},
author={John D. Towers},
journal={SIAM J. Numerical Analysis},
year={2000},
volume={38},
pages={681-698}
}

The subject of this paper is a scalar finite difference algorithm, based on the Godunov or Engquist-Osher flux, for scalar conservation laws where the flux is spatially dependent through a possibly discontinuous coefficient, k. The discretization of k is staggered with respect to the discretization of the conserved quantity u, so that only a scalar Riemann solver is required. The main result of the paper is convergence of a subsequence to a weak solution when the flux is strictly concave andâ€¦Â CONTINUE READING