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Convergence of a difference scheme for conservation laws with a discontinuous flux. (English) Zbl 0972.65060
Convergence is established for a scalar finite difference scheme, based on the Godunov or Enquist-Osher flux, for a scalar conservation law having a flux that is spatially dependent with a possibly discontinuous coefficient. The algorithm uses only scalar Riemann solvers. The limit function is shown to satisfy Kruzkov-type entropy inequalities.

MSC:
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
35R05 PDEs with low regular coefficients and/or low regular data
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