论文标题
动态边界条件的抛物线问题的二阶散装 - 表面分裂
A second-order bulk--surface splitting for parabolic problems with dynamic boundary conditions
论文作者
论文摘要
本文介绍了一种新的方法，用于构建具有动态边界条件的半线性抛物线偏微分方程方程的散装 - 表面分裂方案。拟议的构建基于对系统的重新制定，作为部分差异 - 代数方程，并包含某些延迟术语以进行解耦。为了获得完全离散的方案，分裂方法与空间中的有限元素结合在一起，并在时间内离散化。在本文中，我们将重点放在二阶情况下，导致$ 3 $步骤的方案。我们在弱CFL型条件下证明了二阶收敛性，并通过数值实验确认理论发现。此外，我们以数值说明了高阶分裂方案的潜力。
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.
