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Analysis and approximation of a scalar conservation law with a flux function with discontinuous coefficients. (English) Zbl 1078.35011

The authors study a model of conservative nonlinear conservation laws with a discontinuous flux function. More precisely, the following equation is being studied \(u_t + (k(x)u(1-u))_x = 0.\) The authors find a particular entropy condition which has to be fullfiled on the line of discontinuity of the coefficient \(k\), which guarantees the uniqueness of the entropy solution. Two new finite volume schemes are proposed to simulate the conservation laws with discontinuous coefficients. A comparison with commercial finite volume codes is done. It is shown that a loss of accuaracy of the commercial codes has been detected. A modified MUSCL method for stationary states is introduced as well.

MSC:

35A35 Theoretical approximation in context of PDEs
35L65 Hyperbolic conservation laws
35R05 PDEs with low regular coefficients and/or low regular data
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
76M12 Finite volume methods applied to problems in fluid mechanics
76S05 Flows in porous media; filtration; seepage
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