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.

翻译：本文研究了具有动态边界条件的(半线性)抛物线部分偏差方程式的散状分解方法。提议的 " 谎言分解办法 " 的基础是将问题重新定位为一种结合的局部差价方程系统,即边界条件被视为与大宗问题相伴的第二个动态方程。分解办法与散装表面有限要素和两个子系统的隐性电极分解相结合。我们证明,在以美元/吨/升克/克/赫克/克等值为不变值的CFL条件较弱的情况下,由此形成的完全离散的分解方案在第一线组合。还用Allen-Cahn型的动态边界条件从数字上说明了这种趋同。