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TVD Fluxes for the High-Order ADER Schemes

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Abstract

In this paper we propose to use a TVD flux, instead of a first-order monotone flux, as the building block for designing very high-order methods; we implement the idea in the context of ADER schemes via a new flux expansion. Systematic assessment of the new schemes shows substantial gains in accuracy; these are particularly evident for problems involving long time evolution

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Authors and Affiliations

  1. Laboratory of Applied Mathematics, Faculty of Engineering, University of Trento, Trento, Italy

    E. F. Toro

  2. Department of Mathematics, Faculty of Science, University of Trento, Trento, Italy

    V. A. Titarev

Authors
  1. E. F. Toro
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  2. V. A. Titarev
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Correspondence to E. F. Toro.

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Toro, E.F., Titarev, V.A. TVD Fluxes for the High-Order ADER Schemes. J Sci Comput 24, 285–309 (2005). https://doi.org/10.1007/s10915-004-4790-8

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  • DOI: https://doi.org/10.1007/s10915-004-4790-8

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