On the Energy Stable Approximation of Hamiltonian and Gradient Systems
Abstract: A general framework for the numerical approximation of evolution problems is presented that allows to preserve an underlying dissipative Hamiltonian or gradient structure exactly. The approach relies on rewriting the evolution problem in a particular form that complies with the underlying geometric structure. The Galerkin approximation of a corresponding variational formulation in space then automatically preserves this structure which allows to deduce important properties for appropriate discretization schemes including projection based model order reduction. We further show that the underlying structure is preserved also under time discretization by a Petrov–Galerkin approach. The presented framework is rather general and allows the numerical approximation of a wide range of applications, including nonlinear partial differential equations and port-Hamiltonian systems. Some examples will be discussed for illustration of our theoretical results, and connections to other discretization approaches will be highlighted.
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Bibliographic citation
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On the Energy Stable Approximation of Hamiltonian and Gradient Systems ; volume:21 ; number:2 ; year:2021 ; pages:335-349 ; extent:15
Computational methods in applied mathematics ; 21, Heft 2 (2021), 335-349 (gesamt 15)
- Creator
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Egger, Herbert
Habrich, Oliver
Shashkov, Vsevolod
- DOI
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10.1515/cmam-2020-0025
- URN
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urn:nbn:de:101:1-2410261553546.210141234638
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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15.08.2025, 7:37 AM CEST
Data provider
Deutsche Nationalbibliothek. If you have any questions about the object, please contact the data provider.
Associated
- Egger, Herbert
- Habrich, Oliver
- Shashkov, Vsevolod
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