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On conservation and dual consistency for summation-by-parts based approximations of parabolic problems
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-7972-6183
2019 (English)Report (Other academic)
Abstract [en]

We consider the coupling of parabolic problems discretized using difference operators on summation-by-parts (SBP) form with interface conditions imposed weakly. In [1, 2], it was shown that conservation and dual consistency are equivalent concepts for linear conservation laws. Here, we show that these concepts are equivalent also for symmetric or symmetrizable parabolic problems, exemplified by the heat equation. We rewrite the heat equation as first order system as in the local discontinuous Galerkin method and show the equivalence of dual consistency and conservation for both the first and second order forms.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2019. , p. 9
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2019:5
National Category
Computational Mathematics Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-159529ISRN: LiTH-MAT-R--2019/05--SEOAI: oai:DiVA.org:liu-159529DiVA, id: diva2:1341884
Available from: 2019-08-12 Created: 2019-08-12 Last updated: 2019-08-12Bibliographically approved

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Ghasemi Zinatabadi, FatemehNordström, Jan
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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
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  • Other locale
More languages
Output format
  • html
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