A second-order bulk–surface splitting for parabolic problems with dynamic boundary conditions
- This paper introduces a novel approach for the construction of bulk–surface splitting schemes for semilinear parabolic partial differential equations with dynamic boundary conditions. The proposed construction is based on a reformulation of the system as a partial differential–algebraic equation and the inclusion of certain delay terms for the decoupling. To obtain a fully discrete scheme, the splitting approach is combined with finite elements in space and a backward differentiation formula in time. Within this paper, we focus on the second-order case, resulting in a 3-step scheme. We prove second-order convergence under the assumption of a weak CFL-type condition and confirm the theoretical findings by numerical experiments. Moreover, we illustrate the potential for higher-order splitting schemes numerically.
| Author: | Robert AltmannORCiDGND, Christoph ZimmerORCiDGND |
|---|---|
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/107882 |
| ISSN: | 0272-4979OPAC |
| ISSN: | 1464-3642OPAC |
| Parent Title (English): | IMA Journal of Numerical Analysis |
| Publisher: | Oxford University Press (OUP) |
| Type: | Article |
| Language: | English |
| Date of first Publication: | 2023/08/12 |
| Release Date: | 2023/09/21 |
| Tag: | Applied Mathematics; Computational Mathematics; General Mathematics |
| DOI: | https://doi.org/10.1093/imanum/drad062 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Numerische Mathematik | |
| Latest Publications (not yet published in print): | Aktuelle Publikationen (noch nicht gedruckt erschienen) |
