黏性Cahn-Hilliard方程的二阶BDF数值格式  

Second Order BDF Numerical Scheme for Viscous Cahn-Hilliard Equation

作　　者：郭媛 王旦霞 张建文 GUO Yuan;WANG Danxia;ZHANG Jianwen(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,太原030024

出　　处：《吉林大学学报（理学版）》2023年第5期1063-1072,共10页Journal of Jilin University:Science Edition

基　　金：国际合作基地与平台项目(批准号:202104041101019);山西省回国留学人员科研项目(批准号:2021-029);山西省自然科学基金面上项目(批准号:202203021211129).

摘　　要：采用有限元方法对黏性Cahn-Hilliard方程进行数值求解.首先,引入辅助变量Lagrange乘子r,得到黏性Cahn-Hilliard方程的等价形式;其次,在空间上采用混合有限元逼近,时间上采用隐式向后差分公式(BDF)进行离散,给出黏性Cahn-Hilliard方程的二阶线性有限元数值格式,并分析所给格式的无条件能量稳定性和误差估计;最后,通过一系列数值算例验证所给格式的精确性和有效性.结果表明,该数值格式是理想的,并具有同时满足线性、无条件能量稳定和二阶精度的特点.We used finite element method to numerically solve the viscous Cahn-Hilliard equation.Firstly,the equivalent form of the viscous Cahn-Hilliard equation was obtained by introducing the Lagrange multiplier r of the auxiliary variable.Secondly,the second order linear finite element numerical scheme for the viscous Cahn-Hilliard equation was given by using the mixed finite element approximation in space and the implicit backward differentiation formula(BDF)for discretization in time,and the unconditional stability in energy and error estimation of the given scheme were analyzed in detail.Finally,a series of numerical examples were used to verify the accuracy and effectiveness of the given scheme.The results show that the proposed numerical scheme is ideal and has the characteristics of simultaneously satisfying linear,unconditional stability in energy and second order accuracy.

关 键 词：黏性Cahn-Hilliard方程 LAGRANGE乘子 向后差分公式(BDF) 无条件能量稳定 

分 类 号：O221.6[理学—运筹学与控制论]