TVD Fluxes for the High-Order ADER Schemes

Authors:
E. F. Toro;V. A. Titarev
Affiliations:
Laboratory of Applied Mathematics, Faculty of Engineering, University of Trento, Trento, Italy;Department of Mathematics, Faculty of Science, University of Trento, Trento, Italy
Venue:
Journal of Scientific Computing
Year:
2005

Citing 9
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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