2021/08/18 by Robert Altmann, Balázs Kovács, Altmann, Robert +3
Engineering · Mathematics · #65L80 #65M12 #65M20 #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2108.08147
openalex publication_date 2021/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper studies bulk-surface splitting methods of first order for\n(semi-linear) parabolic partial differential equations with dynamic boundary\nconditions. The proposed Lie splitting scheme is based on a reformulation of\nthe problem as a coupled partial differential-algebraic equation system, i.e.,\nthe boundary conditions are considered as a second dynamic equation which is\ncoupled to the bulk problem. The splitting approach is combined with\nbulk-surface finite elements and an implicit Euler discretization of the two\nsubsystems. We prove first-order convergence of the resulting fully discrete\nscheme in the presence of a weak CFL condition of the form \τ \≤ c h for\nsome constant c>0. The convergence is also illustrated numerically using\ndynamic boundary conditions of Allen-Cahn-type.\n