Cahn-Hilliard方程的新型二阶稳定化半隐有限元方法  

A new second-order stabilized semi-implicit¯nite element method for Cahn-Hilliard equation

作　　者：于悦 张建松 秦荣 YU Yue;ZHANG Jian-Song;QIN Rong(School of Science,China University of Petroleum,Qingdao 266580,China)

机构地区：[1]中国石油大学(华东)理学院,山东青岛266580

出　　处：《高校应用数学学报（A辑）》2023年第3期305-316,共12页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：山东省自然科学基金(ZR2019MA015);中央高校基础研究专项基金(22CX03020A)。

摘　　要：基于Crank-Nicolson/Adams-Bashforth离散,一种新型的二阶稳定化半隐有限元格式被建立用来求解Cahn-Hilliard方程.在此格式中,通过添加一个新型的二阶稳定项,得到一个满足离散的能量耗散定律的线性系统.空间离散考虑Galerkin有限元方法,从而获得时空全离散格式.算法的稳定性被考虑,同时给出相应的误差估计.理论结果表明,所提出的算法具有二阶精度.最后,数值算例验证所提算法的有效性.Based on the Crank-Nicolson/Adams-Bashforth discretization,a new second-order stabilized semi-implicit Galerkin finite element method is presented for the Cahn-Hilliard equation.In this method,by adding a new time second-order stabilization term,the nonlinear terms are treated explicitly.This treatment results into a linear system with constant coefficients,and the resulted algorithm satisfies discrete energy dissipation laws.Afterward,the standard conforming finite element method is used to gain the fully discrete scheme,and then a rigorous error analysis is carried out.Theoretical result shows that the proposed approximation is of time second-order accuracy.Finally,several numerical examples are provided to confirm the efficiency of the proposed method.

关 键 词：稳定化半隐格式 二阶精度 能量稳定 CAHN-HILLIARD方程 

分 类 号：O175.14[理学—数学]