Altmann, Robert ; Kovács, Balázs ; Zimmer, Christoph
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| Dokumentenart: | Artikel |
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| Titel eines Journals oder einer Zeitschrift: | IMA Journal of Numerical Analysis |
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| Verlag: | OXFORD UNIV PRESS |
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| Ort der Veröffentlichung: | OXFORD |
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| Band: | 43 |
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| Nummer des Zeitschriftenheftes oder des Kapitels: | 2 |
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| Seitenbereich: | S. 950-975 |
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| Datum: | 2022 |
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| Institutionen: | Mathematik |
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| Identifikationsnummer: | | Wert | Typ |
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| 10.1093/imanum/drac002 | DOI |
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| Stichwörter / Keywords: | CAHN-HILLIARD EQUATION; DISCRETIZATION; dynamic boundary conditions; PDAE; splitting methods; bulk-surface splitting; parabolic equations |
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| Dewey-Dezimal-Klassifikation: | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
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| Status: | Veröffentlicht |
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| Begutachtet: | Ja, diese Version wurde begutachtet |
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| An der Universität Regensburg entstanden: | Ja |
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| Dokumenten-ID: | 75324 |
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Zusammenfassung
This paper studies bulk-surface splitting methods of first order for (semilinear) parabolic partial differential equations with dynamic boundary conditions. The proposed Lie splitting scheme is based on a reformulation of the problem as a coupled partial differential-algebraic equation system, i.e., the boundary conditions are considered as a second dynamic equation that is coupled to the bulk ...
Zusammenfassung
This paper studies bulk-surface splitting methods of first order for (semilinear) parabolic partial differential equations with dynamic boundary conditions. The proposed Lie splitting scheme is based on a reformulation of the problem as a coupled partial differential-algebraic equation system, i.e., the boundary conditions are considered as a second dynamic equation that is coupled to the bulk problem. The splitting approach is combined with bulk-surface finite elements and an implicit Euler discretization of the two subsystems. We prove first-order convergence of the resulting fully discrete scheme in the presence of a weak CFL condition of the form tau <= ch for some constant c > 0. The convergence is also illustrated numerically using dynamic boundary conditions of Allen-Cahn type.
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