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Error Boundedness of Discontinuous Galerkin Spectral Element Approximations of Hyperbolic Problems
Department of Mathematics, The Florida State University.
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-7972-6183
Mathematisches Institut, Universität zu Köln.
2017 (English)In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 72, no 1, p. 314-330Article in journal (Refereed) Published
Abstract [en]

We examine the long time error behavior of discontinuous Galerkin spectral element approximations to hyperbolic equations. We show that the choice of numerical flux at interior element boundaries affects the growth rate and asymptotic value of the error. Using the upwind flux, the error reaches the asymptotic value faster, and to a lower value than a central flux gives, especially for low resolution computations. The differences in the error caused by the numerical flux choice decrease as the solution becomes better resolved.

Place, publisher, year, edition, pages
2017. Vol. 72, no 1, p. 314-330
Keywords [en]
Discontinuous Galerkin spectral element method, Energy stability, Error growth, Error bound, Hyperbolic problems
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-133875DOI: 10.1007/s10915-017-0358-2ISI: 000403410200013OAI: oai:DiVA.org:liu-133875DiVA, id: diva2:1064841
Available from: 2017-01-13 Created: 2017-01-13 Last updated: 2018-01-12Bibliographically approved

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CiteExportLink to record
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  • apa
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