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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
##### Keywords:
compensated compactness
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##### References:
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