| Autor: |
Altmann, Robert, Kovács, Balázs, Zimmer, Christoph |
| Rok vydání: |
2021 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
This paper studies bulk-surface splitting methods of first order for (semi-linear) 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 which 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 $\tau \leq c h$ for some constant $c>0$. The convergence is also illustrated numerically using dynamic boundary conditions of Allen-Cahn-type. |
| Databáze: |
arXiv |
| Externí odkaz: |
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