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 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∞ and BV norms with respect to the relaxation parameter. The relaxation limit is also investigated.
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Aregba-Driollet et al. (1996) studied this question.
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