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Mesh Redistribution Strategies and Finite Element Schemes for Hyperbolic Conservation Laws

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Abstract

In this work we consider a new class of Relaxation Finite Element schemes for hyperbolic conservation laws, with more stable behavior on the limit area of the relaxation parameter. Combining 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 parameter where the scheme lacks of the relaxation mechanism. Thus we experimentally conclude that the proposed spatial redistribution process, has by its own interesting stabilization properties for computational solutions of conservation law problems.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Cyprus, 1678, Nicosia-Cyprus, Greece

    Christos Arvanitis

  2. Institute of Applied and Computational Mathematics, FORTH, 71110, Heraklion, Crete, Greece

    Christos Arvanitis

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  1. Christos Arvanitis
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Arvanitis, C. Mesh Redistribution Strategies and Finite Element Schemes for Hyperbolic Conservation Laws. J Sci Comput 34, 1–25 (2008). https://doi.org/10.1007/s10915-007-9155-7

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  • DOI: https://doi.org/10.1007/s10915-007-9155-7

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