求解含对数势和变流动系数的Cahn-Hilliard-Hele-Shaw系统的解耦有限元方法  

A decoupling method for solving Cahn-Hilliard-Hele-Shaw system with logarithmic potential and variable mobility

作　　者：郭亚瑜 贾宏恩 GUO Yayu;JIA Hongen(College of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China)

机构地区：[1]太原理工大学数学学院

出　　处：《西安理工大学学报》2019年第4期506-511,共6页Journal of Xi'an University of Technology

基　　金：国家自然科学基金面上资助项目(11872264);国家自然科学基金青年基金资助项目(11401422)

摘　　要：本文提出了一种解耦方法用来求解含对数势和变系数的Cahn-Hilliard-Hele-Shaw系统。在时间上采用基于对能量泛函的凸分裂进行离散,空间上利用混合有限元方法进行离散。通过一种压力投影算法更新Darcy方程中的压力梯度,使得在每一个时间步上只需要求解一个Possion方程。对于对数势,利用正则化方法,将自由能密度函数的定义域进行延拓。并证明了格式的稳定性。最后给出了一系列的数值算例来验证理论分析。In this paper,a decoupling of the mixed finite element method for solving Cahn-Hilliard-Hele-Shaw system with logarithmic potential and variable mobility is proposed.The temporal discretization of the Cahn-Hilliard equation is based on a convex-splitting of the energy functional with the mixed finite element method used in space.By using the pressure projection technique,the pressure gradient is updated in Darcy equation so that at each time step we just need to solve a Possion equation.For the logarithmic potential,we make the domain for the density function of free energy,which is extended by using the regularization procedure.Further,the stability of the proposed methods are established.Finally,numerical experiments are conducted to illustrate the theoretical analysis.

关 键 词：对数势 Cahn-Hilliard-Hele-Shaw系统 变系数 解耦 

分 类 号：O241.82[理学—计算数学]