论文标题
具有动态边界条件的Cahn--Hilliard方程的耗散性离散化
Dissipation-preserving discretization of the Cahn--Hilliard equation with dynamic boundary conditions
论文作者
论文摘要
本文介绍了与三种不同类型的动态边界条件的Cahn--Hilliard方程的时间步进方案。一阶和二阶的提议方案是质量保守和能量散文的，并且 - 由于它们基于公式作为部分微分方程的耦合系统，因此可以在整体和边界中进行不同的空间离散。后者可以在边界上进行改进，而无需在域内内部的网格适应。在数值实验中说明了所得的计算增益。
This paper deals with time stepping schemes for the Cahn--Hilliard equation with three different types of dynamic boundary conditions. The proposed schemes of first and second order are mass-conservative and energy-dissipative and -- as they are based on a formulation as a coupled system of partial differential equations -- allow different spatial discretizations in the bulk and on the boundary. The latter enables refinements on the boundary without an adaptation of the mesh in the interior of the domain. The resulting computational gain is illustrated in numerical experiments.
