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The crucial role of...
The crucial role of Lagrange multipliers in a space-time symmetry preserving discretization scheme for IVPs
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- Rothkopf, Alexander (author)
- Faculty of Science and Technology, University of Stavanger, 4021 Stavanger, Norway
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- Nordström, Jan, 1953- (author)
- Linköpings universitet,Tekniska fakulteten,Tillämpad matematik,Department of Mathematics and Applied Mathematics, University of Johannesburg, Johannesburg, South Africa
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(creator_code:org_t)
- Elsevier, 2024
- 2024
- English.
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In: Journal of Computational Physics. - : Elsevier. - 0021-9991 .- 1090-2716. ; 511
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Abstract
Subject headings
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- In a recently developed variational discretization scheme for second order initial value problems, it was shown that the Noether charge associated with time translation symmetry is exactly preserved in the interior of the simulated domain. The obtained solution also fulfils the naively discretized equations of motions inside the domain, except for the last two grid points. Here we provide an explanation for the deviations at the boundary as stemming from the effect of Lagrange multipliers used to implement initial and connecting conditions. We show explicitly that the Noether charge including the boundary corrections is exactly preserved at its continuum value over the whole simulation domain, including the boundary points.
Subject headings
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Keyword
- Initial value problem
- Lagrange multipliers
- Summation-by-parts
- Noether charge
- Symmetry
Publication and Content Type
- ref (subject category)
- art (subject category)
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