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Convergence of relaxation schemes for conservation laws. (English) Zbl 0872.65086
We study the stability and the convergence for a class of relaxing numerical schemes for conservation laws. Following the approach recently proposed by S. Jin and Z. Xin [Commun. Pure Appl. Math. 48, No. 3, 235-276 (1995; Zbl 0826.65078)], we use a semilinear local relaxation approximation, with a stiff lower order term, and we construct some numerical first and second order accurate algorithms, which are uniformly bounded in the \(L^\infty\) and BV norms with respect to the relaxation parameter. The relaxation limit is also investigated.

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
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