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Summation-by-Parts ...
Summation-by-Parts Operators for General Function Spaces
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- Glaubitz, Jan (author)
- Dartmouth College, Hanover, USA.
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- Nordström, Jan, 1953- (author)
- Linköpings universitet,Tekniska fakulteten,Tillämpad matematik,University of Johannesburg, South Africa.
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- Öffner, Philipp (author)
- Johannes Gutenberg University, Mainz, Germany.
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Dartmouth College, Hanover, USA Tekniska fakulteten (creator_code:org_t)
- Society for Industrial and Applied Mathematics, 2023
- 2023
- English.
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In: SIAM Journal on Numerical Analysis. - : Society for Industrial and Applied Mathematics. - 0036-1429 .- 1095-7170. ; 61:2, s. 733-754
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Abstract
Subject headings
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- Summation-by-parts (SBP) operators are popular building blocks for systematically developing stable and high-order accurate numerical methods for time-dependent differential equations. The main idea behind existing SBP operators is that the solution is assumed to be well approximated by polynomials up to a certain degree, and the SBP operator should therefore be exact for them. However, polynomials might not provide the best approximation for some problems, and other approximation spaces may be more appropriate. In this paper, a theory for SBP operators based on general function spaces is developed. We demonstrate that most of the established results for polynomial-based SBP operators carry over to this general class of SBP operators. Our findings imply that the concept of SBP operators can be applied to a significantly larger class of methods than is currently known. We exemplify the general theory by considering trigonometric, exponential, and radial basis functions.
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Keyword
- summation-by-parts operators
- mimetic discretization
- general function spaces
- trigonometric functions
- exponential functions
- radial basis functions
Publication and Content Type
- ref (subject category)
- art (subject category)
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