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A relaxation scheme for conservation laws with a discontinuous coefficient. (English) Zbl 1078.65076
The authors study a relaxation scheme for conservation laws with discontinuous flux function \(f(k(x),u)\), where \(k(x)\) is a discontinuous coefficient. If \(k \in \text{BV}\) they are able to show that the approximate solutions of the relaxation scheme converge to a weak solution. The Murat-Tartar compensated compactness approach is used in order to prove convergence of their relaxation approximations. Finally, some numerical results are presented in order to demonstrate the convergence.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
35L45 Initial value problems for first-order hyperbolic systems
35R05 PDEs with low regular coefficients and/or low regular data
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