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Convergence of the Lax-Friedrichs scheme and stability for conservation laws with a discontinuous space-time dependent flux. (English) Zbl 1112.65085
The paper presents a convergence proof for the Lax-Friedrichs finite difference scheme in the context of non-convex genuinely nonlinear scalar conservation laws of the form \[ u_t+ f(k(x, t),u)_x= 0, \] where the coefficient \(k(x, t)\) is allowed to be discontinuous along curves in the \((x, t)\) plane. It is shown that a convergent subsequence of approximations produced by the Lax-Friedrichs scheme converges to an entropy solution, implying that the entire computed sequence converges.

MSC:
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
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