Kühn, Martin Joachim und Kruse, Carola und Rüde, Ulrich (2021) Energy-Minimizing, Symmetric Discretizations for Anisotropic Meshes and Energy Functional Extrapolation. SIAM Journal on Scientific Computing, 43 (4), A2448-A2473. SIAM - Society for Industrial and Applied Mathematics. doi: 10.1137/21M1397520. ISSN 1064-8275.
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Offizielle URL: https://epubs.siam.org/doi/abs/10.1137/21M1397520
Kurzfassung
Self-adjoint differential operators often arise from variational calculus on energy functionals. In this case, a direct discretization of the energy functional induces a discretization of the differential operator. Following this approach, the discrete equations are naturally symmetric if the energy functional was self-adjoint, a property that may be lost when using standard difference formulas on nonuniform meshes or when the differential operator has varying coefficients. Low order finite difference or finite element systems can be derived by this approach in a systematic way and on logically structured meshes they become compact difference formulas. Extrapolation formulas used on the discrete energy can then lead to higher oder approximations of the differential operator. A rigorous analysis is presented for extrapolation used in combination with nonstandard integration rules for finite elements. Extrapolation can likewise be applied on matrix-free finite difference stencils. In our applications, both schemes show up to quartic order of convergence.
elib-URL des Eintrags: | https://elib.dlr.de/143792/ | ||||||||||||||||
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Dokumentart: | Zeitschriftenbeitrag | ||||||||||||||||
Titel: | Energy-Minimizing, Symmetric Discretizations for Anisotropic Meshes and Energy Functional Extrapolation | ||||||||||||||||
Autoren: |
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Datum: | 13 Juli 2021 | ||||||||||||||||
Erschienen in: | SIAM Journal on Scientific Computing | ||||||||||||||||
Referierte Publikation: | Ja | ||||||||||||||||
Open Access: | Ja | ||||||||||||||||
Gold Open Access: | Nein | ||||||||||||||||
In SCOPUS: | Ja | ||||||||||||||||
In ISI Web of Science: | Ja | ||||||||||||||||
Band: | 43 | ||||||||||||||||
DOI: | 10.1137/21M1397520 | ||||||||||||||||
Seitenbereich: | A2448-A2473 | ||||||||||||||||
Verlag: | SIAM - Society for Industrial and Applied Mathematics | ||||||||||||||||
ISSN: | 1064-8275 | ||||||||||||||||
Status: | veröffentlicht | ||||||||||||||||
Stichwörter: | partial differential equation, energy functional, symmetry, anisotropy, extrapolation, finite differences, finite elements | ||||||||||||||||
HGF - Forschungsbereich: | Luftfahrt, Raumfahrt und Verkehr | ||||||||||||||||
HGF - Programm: | Raumfahrt | ||||||||||||||||
HGF - Programmthema: | Technik für Raumfahrtsysteme | ||||||||||||||||
DLR - Schwerpunkt: | Raumfahrt | ||||||||||||||||
DLR - Forschungsgebiet: | R SY - Technik für Raumfahrtsysteme | ||||||||||||||||
DLR - Teilgebiet (Projekt, Vorhaben): | R - Aufgaben SISTEC | ||||||||||||||||
Standort: | Köln-Porz | ||||||||||||||||
Institute & Einrichtungen: | Institut für Softwaretechnologie Institut für Softwaretechnologie > High-Performance Computing | ||||||||||||||||
Hinterlegt von: | Kühn, Dr. Martin Joachim | ||||||||||||||||
Hinterlegt am: | 09 Sep 2021 11:36 | ||||||||||||||||
Letzte Änderung: | 20 Jun 2024 13:39 |
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