Altmann, Robert and Kovacs, Balazs and Zimmer, Christoph (2023) Bulk-surface Lie splitting for parabolic problems with dynamic boundary conditions. IMA JOURNAL OF NUMERICAL ANALYSIS, 43 (2). pp. 950-975. ISSN 0272-4979, 1464-3642
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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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | CAHN-HILLIARD EQUATION; DISCRETIZATION; dynamic boundary conditions; PDAE; splitting methods; bulk-surface splitting; parabolic equations |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 21 Feb 2024 06:45 |
| Last Modified: | 21 Feb 2024 06:45 |
| URI: | https://pred.uni-regensburg.de/id/eprint/57712 |
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