粘性Cahn-Hilliard方程的二阶凸分裂有限元格式  

A Second-Order Convex Splitting Finite Element Scheme for the Viscous Cahn-Hilliard Equation

作　　者：苗妮 张建文 王旦霞 MIAO Ni;ZHANG Jianwen;WANG Danxia(College of Mathematics,Taiyuan University of Technology,Jinzhong 030600,China)

机构地区：[1]太原理工大学数学学院,山西晋中030600

出　　处：《应用数学》2023年第3期602-612,共11页Mathematica Applicata

基　　金：山西省回国留学人员科研资助项目(2021-029);山西省国际合作基地与平台项目(202104041101019);山西省基础研究计划(202203021211129)。

摘　　要：本文对粘性Cahn-Hilliard方程提出二阶向后差分格式(BDF)的数值逼近,其中对双阱势函数采用凸分裂方法进行离散.首先,给出离散格式能量稳定性和收敛性的理论分析;其次计算出时间收敛阶和空间收敛阶都趋近于2,这与误差估计的结果一致;最后,通过粗化过程的数值算例,验证了格式的有效性.In this paper,we propose a second-order backward difference formula(BDF)numerical approximation for the viscous Cahn-Hilliard equation,where a convex splitting method is used to discretize the double-well potential function.Firstly,the energy stability and convergence are analyzed in theory.Then,by calculation the temporal and spatial convergence rates are close to 2,which is consistent with the result of error estimation.Finally,we give the numerical simulation of coarsening process to verify the validity of the scheme.

关 键 词：粘性Cahn-Hilliard方程 能量稳定 凸分裂方法 二阶精确 

分 类 号：O241.82[理学—计算数学]