Conservation laws III: relaxation limit

Relaxation Limit for Piecewise Smooth Solutions to Systems of Conservation Laws

In this paper we study the asymptotic equivalence of a general system of 1-D conservation laws and the corresponding relaxation model proposed by S. Jin and Z. Xin (1995, Comm. Pure Appl. Math. 48, 235 277) in the limit of small relaxation rate. It is shown that if the relaxation system satisfies the subcharacteristic condition and the solution of the hyperbolic conservation laws is piecewise s...

A BGK approximation to scalar conservation laws with discontinuous flux

We study the BGK approximation to first-order scalar conservation laws with a flux which is discontinuous in the space variable. We show that the Cauchy Problem for the BGK approximation is well-posed and that, as the relaxation parameter tends to 0, it converges to the (entropy) solution of the limit problem.

Mesh Redistribution Strategies and Finite Element Schemes for Hyperbolic Conservation Laws

In this work we consider a new class of Relaxation Finite Element schemes for Conservation Laws, with more stable behavior on the limit area of the relaxation parameter. Combine this scheme with an efficient adapted spatial redistribution process, considered also in this work, we form a robust scheme of controllable resolution. The results on a number of test problems show that this scheme can ...

Convergence of Relaxation Schemes for Conservation Laws

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 stii lower order term, and we construct some numerical rst and second order accurate algorithms, which are uniformly bounded in the L 1 and BV norms with respect to th...

Scalar conservation laws with a degenerate source: Traveling waves, large-time behavior and zero relaxation limit