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Analysis of the SBP...
Analysis of the SBP-SAT Stabilization for Finite Element Methods Part II: Entropy Stability
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- Abgrall, Remi (author)
- University of Zurich, Switzerland
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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)
- University of Zurich, Switzerland
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- Tokareva, Svetlana (author)
- Los Alamos National Laboratory, USA
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(creator_code:org_t)
- 2021-01-03
- 2023
- English.
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In: Communications on Applied Mathematics and Computation. - : Springer. - 2096-6385 .- 2661-8893. ; 5:2, s. 573-595
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Abstract
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- In the hyperbolic research community, there exists the strong belief that a continuous Galerkin scheme is notoriously unstable and additional stabilization terms have to be added to guarantee stability. In the first part of the series [6], the application of simultaneous approximation terms for linear problems is investigated where the boundary conditions are imposed weakly. By applying this technique, the authors demonstrate that a pure continuous Galerkin scheme is indeed linearly stable if the boundary conditions are imposed in the correct way. In this work, we extend this investigation to the nonlinear case and focus on entropy conservation. By switching to entropy variables, we provide an estimation of the boundary operators also for nonlinear problems, that guarantee conservation. In numerical simulations, we verify our theoretical analysis.
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Publication and Content Type
- ref (subject category)
- art (subject category)
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