Adaptive operator splitting finite element method for Allen-Cahn equation

被引：10
|
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.
引用
收藏
页码：1290 / 1300
页数：11
相关论文
共 50 条
  • [1] An adaptive discontinuous finite volume element method for the Allen-Cahn equation
    Li, Jian
    Zeng, Jiyao
    Li, Rui
    ADVANCES IN COMPUTATIONAL MATHEMATICS, 2023, 49 (04)
  • [2] An adaptive discontinuous finite volume element method for the Allen-Cahn equation
    Jian Li
    Jiyao Zeng
    Rui Li
    Advances in Computational Mathematics, 2023, 49
  • [3] The adaptive SAV weak Galerkin finite element method for the Allen-Cahn equation
    Liu, Ying
    Shen, Xiaoqin
    Guan, Zhen
    Nie, Yufeng
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2023, 151 : 449 - 460
  • [4] Analysis of the operator splitting scheme for the Allen-Cahn equation
    Weng, Zhifeng
    Tang, Longkun
    NUMERICAL HEAT TRANSFER PART B-FUNDAMENTALS, 2016, 70 (05) : 472 - 483
  • [5] Numerical approximation of the conservative Allen-Cahn equation by operator splitting method
    Weng, Zhifeng
    Zhuang, Qingqu
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2017, 40 (12) : 4462 - 4480
  • [6] A finite element method for Allen-Cahn equation on deforming surface
    Olshanskii, Maxim
    Xu, Xianmin
    Yushutin, Vladimir
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2021, 90 : 148 - 158
  • [7] A two-level finite element method for the Allen-Cahn equation
    Liu, Qingfang
    Zhang, Ke
    Wang, Zhiheng
    Zhao, Jiakun
    INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2019, 96 (01) : 158 - 169
  • [8] A SCR-based error estimation and adaptive finite element method for the Allen-Cahn equation
    Chen, Yaoyao
    Huang, Yunqing
    Yi, Nianyu
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2019, 78 (01) : 204 - 223
  • [9] Recovery type a posteriori error estimation of adaptive finite element method for Allen-Cahn equation
    Chen, Yaoyao
    Huang, Yunqing
    Yi, Nianyu
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2020, 369
  • [10] Comparison of operator splitting schemes for the numerical solution of the Allen-Cahn equation
    Ayub, Sana
    Affan, Hira
    Shah, Abdullah
    AIP ADVANCES, 2019, 9 (12)
12345