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On the convergence ...
On the convergence rates of energy-stable finite-difference schemes
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- Svärd, Magnus (author)
- Dept. of Mathematics, University of Bergen, Bergen, Norway
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- Nordström, Jan, 1953- (author)
- Linköpings universitet,Beräkningsmatematik,Tekniska fakulteten
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Dept of Mathematics, University of Bergen, Bergen, Norway Beräkningsmatematik (creator_code:org_t)
- Elsevier, 2019
- 2019
- English.
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In: Journal of Computational Physics. - : Elsevier. - 0021-9991 .- 1090-2716. ; 397
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Abstract
Subject headings
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- 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.
Subject headings
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Keyword
- Finite difference
- Stability
- Convergence rate
- Consistency
- Energy stability
Publication and Content Type
- ref (subject category)
- art (subject category)
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