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 produce entropic-approximations of high resolution even on the limit of the relaxation parameters. Since on the limit the scheme lack of the relaxation mechanism, we experimentally conclude that the proposed spatial redistribution can be a stabilization mechanism by its own for computational solutions of CL problems.