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Review of summation-by-parts schemes for initial-boundary-value problems
Department of Mathematics, University of Bergen.
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-7972-6183
2014 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 268, 17-38 p.Article in journal (Refereed) Published
Abstract [en]

High-order finite difference methods are efficient, easy to program, scale well in multiple dimensions and can be modified locally for various reasons (such as shock treatment for example). The main drawback has been the complicated and sometimes even mysterious stability treatment at boundaries and interfaces required for a stable scheme. The research on summation-by-parts operators and weak boundary conditions during the last 20 years has removed this drawback and now reached a mature state. It is now possible to construct stable and high order accurate multi-block finite difference schemes in a systematic building-block-like manner. In this paper we will review this development, point out the main contributions and speculate about the next lines of research in this area.

Place, publisher, year, edition, pages
Linköping University Electronic Press, 2014. Vol. 268, 17-38 p.
Keyword [en]
Well posed problems; Energy estimates; Finite difference; Finite volume; Boundary conditions; Interface conditions; Stability; High order of accuracy
National Category
Computational Mathematics
URN: urn:nbn:se:liu:diva-104966DOI: 10.1016/ 000334586800002OAI: diva2:701790
Available from: 2014-03-04 Created: 2014-03-04 Last updated: 2014-05-28

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