1. A second-order bulk--surface splitting for parabolic problems with dynamic boundary conditions
- Author
-
Altmann, R. and Zimmer, C.
- Subjects
Mathematics - Numerical Analysis ,65M12, 65L80, 65M20 - Abstract
This paper introduces a novel approach for the construction of bulk--surface splitting schemes for semi-linear 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 BDF discretization 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., Comment: accepted for publication in IMA J. Numer. Anal
- Published
- 2022