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On the order of Acc...
On the order of Accuracy of Finite Difference Operators on Diagonal Norm Based Summation-By-Parts Form
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- Linders, Viktor, 1988- (author)
- Linköpings universitet,Beräkningsmatematik,Tekniska fakulteten
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- Lundquist, Tomas (author)
- University of Cape Town, South Africa
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- Nordström, Jan, 1953- (author)
- Linköpings universitet,Beräkningsmatematik,Tekniska fakulteten
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(creator_code:org_t)
- Linköping : Linköping University Electronic Press, 2017
- English 15 s.
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Series: LiTH-MAT-R, 0348-2960 ; 2017:11
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Abstract
Subject headings
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- In this paper we generalise 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.
Subject headings
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Keyword
- Finite difference schemes
- summation-by-parts operators
- numerical differentiation
- quadrature rules
- order of accuracy
Publication and Content Type
- vet (subject category)
- rap (subject category)
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