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On the order of Accuracy of Finite Difference Operators on Diagonal Norm Based Summation-by-Parts Form
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.
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-7972-6183
2018 (English)In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 56, no 2, p. 1048-1063Article in journal (Refereed) Published
Abstract [en]

In this paper we generalize results regarding the order of accuracy of finite difference operators on summation-by-parts (SBP) form, previously known to hold on uniform grids, to grids with arbitrary point distributions near domain boundaries. We give a definite proof that the order of accuracy in the interior of a diagonal norm based SBP operator must be at least twice that of the boundary stencil, irrespective of the grid point distribution near the boundary. Additionally, we prove that if the order of accuracy in the interior is precisely twice that of the boundary, then the diagonal norm defines a quadrature rule of the same order as the interior stencil. Again, this result is independent of the grid point distribution near the domain boundaries.

Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics, 2018. Vol. 56, no 2, p. 1048-1063
Keywords [en]
finite dierence schemes, summation-by-parts operators, numerical differentiation, quadrature rules, order of accuracy
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-147643DOI: 10.1137/17M1139333ISI: 000431189500017OAI: oai:DiVA.org:liu-147643DiVA, id: diva2:1202947
Available from: 2018-05-02 Created: 2018-05-02 Last updated: 2018-05-23

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Linders, ViktorLundquist, TomasNordström, Jan

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  • apa
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