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A stable and dual consistent boundary treatment using finite differences on summation-by-parts form
Uppsala University, Department of Information Technology.
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-7972-6183
2012 (English)In: European Congress on Computational Methods in Applied Sciences and Engineering, Vienna University of Technology , 2012Conference paper, Published paper (Other academic)
Abstract [en]

This paper is concerned with computing very high order accurate linear functionals from a numerical solution of a time-dependent partial differential equation (PDE). Based on finite differences on summation-by-parts form, together with a weak implementation of the boundary conditions, we show how to construct suitable boundary conditions for the PDE such that the continuous problem is well-posed and the discrete problem is stable and spatially dual consistent. These two features result in a superconvergent functional, in the sense that the order of accuracy of the functional is provably higher than that of the solution.

Place, publisher, year, edition, pages
Vienna University of Technology , 2012.
Keyword [en]
Superconvergence, functionals, summation-by-parts, weak boundary conditions, stability, dual consistency
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-81890ISBN: 978-3-9503537-0-9 (print)OAI: oai:DiVA.org:liu-81890DiVA: diva2:556560
Conference
(ECCOMAS 2012) J. Eberhardsteiner et.al. (eds.) Vienna, Austria, September 10-14, 2012
Available from: 2012-09-25 Created: 2012-09-24 Last updated: 2016-09-09

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Nordström, Jan

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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf