2022/09/16 by R. Altmann, Altmann, R., Christoph Zimmer +1
Mathematics · Engineering · #Differential Equations and Numerical Methods #Advanced Numerical Methods in Computational Mathematics #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2209.07835
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.