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The Relation Between Primal and Dual Boundary Conditions for Hyperbolic Systems of Equations
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]

In this paper we study boundary conditions for linear hyperbolic systems of equations and the corresponding dual problems. In particular, we show that the primal and dual boundary conditions are related by a simple scaling relation. It is also shown that the weak dual problem can be derived directly from the weak primal problem.

Based on the continuous analysis, we discretize and perform computations with a high-order finite difference scheme on summation-by-parts form with weak boundary conditions. It is shown that the results obtained in the continuous analysis lead directly to stability results for the primal and dual discrete problems. Numerical experiments corroborate the theoretical results.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2019. , p. 22
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2019:6
Keywords [en]
Hyperbolic systems, boundary conditions, primal problem, dual problem, well-posedness, dual consistency
National Category
Computational Mathematics Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-158904ISRN: LiTH-MAT-R--2019/06--SEOAI: oai:DiVA.org:liu-158904DiVA, id: diva2:1337834
Available from: 2019-07-17 Created: 2019-07-17 Last updated: 2019-11-01Bibliographically approved

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The Relation Between Primal and Dual Boundary Conditions for Hyperbolic Systems of Equations(569 kB)44 downloads
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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
  • 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
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  • asciidoc
  • rtf