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On the convergence rates of energy-stable finite-difference schemes
Dept. of Mathematics, University of Bergen, Bergen, Norway.
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-7972-6183
2019 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 397, article id 108819Article in journal (Refereed) Published
Abstract [en]

We consider constant-coefficient initial-boundary value problems, with a first or second derivative in time and a highest spatial derivative of order q, and their semi-discrete finite difference approximations. With an internal truncation error of order p≥1, and a boundary error of order r≥0, we prove that the convergence rate is: min⁡(p,r+q). The assumptions needed for these results to hold are: i) The continuous problem is linear and well-posed (with a smooth solution). ii) The numerical scheme is consistent, nullspace consistent, nullspace invariant, and energy stable. These assumptions are often satisfied for Summation-By-Parts schemes.

Place, publisher, year, edition, pages
Elsevier, 2019. Vol. 397, article id 108819
Keywords [en]
Finite difference, Stability, Convergence rate, Consistency, Energy stability
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-159802DOI: 10.1016/j.jcp.2019.07.018OAI: oai:DiVA.org:liu-159802DiVA, id: diva2:1344778
Available from: 2019-08-22 Created: 2019-08-22 Last updated: 2019-08-22

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CiteExportLink to record
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  • apa
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  • de-DE
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