Adaptive operator splitting finite element method for Allen-Cahn equation

被引：11
|
作者：
Huang, Yunqing [1 ]
Yang, Wei [1 ]
Wang, Hao [1 ]
Cui, Jintao [2 ,3 ]
机构：
[1] Xiangtan Univ, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan, Peoples R China
[2] Hong Kong Polytech Univ, Dept Appl Math, Hung Hom, TU829,Block T,11 Yuk Choi Rd, Hong Kong, Peoples R China
[3] Hong Kong Polytech Univ, Dept Appl Math, Shenzhen Res Inst, Shenzhen, Peoples R China
来源：
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2019年 / 35卷 / 03期
基金：
中国国家自然科学基金;
关键词：
adaptive algorithm; Allen-Cahn equation; finite element method; operator splitting; SCR;
D O I：
10.1002/num.22350
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, a new numerical method is proposed and analyzed for the Allen-Cahn (AC) equation. We divide the AC equation into linear section and nonlinear section based on the idea of operator splitting. For the linear part, it is discretized by using the Crank-Nicolson scheme and solved by finite element method. The nonlinear part is solved accurately. In addition, a posteriori error estimator of AC equation is constructed in adaptive computation based on superconvergent cluster recovery. According to the proposed a posteriori error estimator, we design an adaptive algorithm for the AC equation. Numerical examples are also presented to illustrate the effectiveness of our adaptive procedure.
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页码：1290 / 1300
页数：11
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