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 and… CONTINUE READING
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