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REVIEW OF SUMMATION-BY-PARTS SCHEMES FOR INITIAL-BOUNDARY-VALUE PROBLEMS
Department of Mathematics, University of Bergen, Norway.
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.
2013 (English)Report (Other academic)
Abstract [en]

High-order finite difference methods are efficient, easy to program, scales well in multiple dimensions and can be modified locally for various reasons (such as shock treatment for example). The main drawback have been the complicated and sometimes even mysterious stability treatment at boundaries and interfaces required for a stable scheme. The research on summation-byparts operators and weak boundary conditions during the last 20 years have 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: Linköping University Electronic Press, 2013. , 28 p.
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2013:15
Keyword [en]
well posed problems, energy estimates, finite difference; finite volume; boundary conditions; interface conditions; stability; high order of accuracy
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-101956ISRN: LiTH-MAT-R--2013/15--SEOAI: oai:DiVA.org:liu-101956DiVA: diva2:666933
Available from: 2013-11-25 Created: 2013-11-25 Last updated: 2013-12-12Bibliographically approved

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REVIEW OF SUMMATION-BY-PARTS SCHEMES FOR INITIAL-BOUNDARY-VALUE PROBLEMS(1214 kB)316 downloads
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CiteExportLink to record
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Citation style
  • apa
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Output format
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