Abstract In this paper, we develop a novel second order in time, decoupled, energy stable finite element scheme for simulation of Cahn-Hilliard-Hele-Shaw system. The idea of scalar auxiliary variable approach is introduced to handle the nonlinear bulk. An operator-splitting strategy is utilized to fully decouple the coupled Cahn-Hilliard equation and Darcy equation. A full discretization is built in the framework of Galerkin finite element method. The unique solvability of numerical solution and preservation of energy law are rigorously established. Numerical experiences are recorded to illustrate the features of the designed numerical method, verify the theoretical results and conduct realistic applications.

中文翻译：

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Cahn-Hilliard-Hele-Shaw系统的二阶解耦能量稳定数值格式

摘要 在本文中，我们为 Cahn-Hilliard-Hele-Shaw 系统的仿真开发了一种新的时间二阶解耦能量稳定有限元方案。引入标量辅助变量方法的思想来处理非线性体积。使用算子分裂策略来完全解耦耦合的 Cahn-Hilliard 方程和 Darcy 方程。在 Galerkin 有限元方法的框架内建立了完全离散化。数值解的唯一可解性和能量守恒定律得到严格建立。记录了数值经验，以说明所设计数值方法的特点，验证理论结果并进行实际应用。