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
  • [21] THE STABILIZED SEMI-IMPLICIT FINITE ELEMENT METHOD FOR THE SURFACE ALLEN-CAHN EQUATION
    Xiao, Xufeng
    Feng, Xinlong
    Yuan, Jinyun
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2017, 22 (07): : 2857 - 2877
  • [22] A two-grid finite element method for the Allen-Cahn equation with the logarithmic potential
    Wang, Danxia
    Li, Yanan
    Jia, Hongen
    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2023, 39 (02) : 1251 - 1265
  • [23] Efficient Implementation and Numerical Analysis of Finite Element Method for Fractional Allen-Cahn Equation
    Wang, Guozhen
    Chen, Huanzhen
    MATHEMATICAL PROBLEMS IN ENGINEERING, 2019, 2019
  • [24] An efficient nonconforming finite element two-grid method for Allen-Cahn equation
    Shi Dongyang
    Liu Qian
    APPLIED MATHEMATICS LETTERS, 2019, 98 : 374 - 380
  • [25] An explicit stable finite difference method for the Allen-Cahn equation
    Lee, Chaeyoung
    Choi, Yongho
    Kim, Junseok
    APPLIED NUMERICAL MATHEMATICS, 2022, 182 : 87 - 99
  • [26] Convergence of Exponential Attractors for a Finite Element Approximation of the Allen-Cahn Equation
    Pierre, Morgan
    NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2018, 39 (16) : 1755 - 1784
  • [27] ADAPTIVE DISCONTINUOUS GALERKIN FINITE ELEMENTS FOR ADVECTIVE ALLEN-CAHN EQUATION
    Uzunca, Murat
    Sariaydin-Filibelioglu, Ayse
    NUMERICAL ALGEBRA CONTROL AND OPTIMIZATION, 2021, 11 (02): : 269 - 281
  • [28] An unconditionally energy stable second order finite element method for solving the Allen-Cahn equation
    Li, Congying
    Huang, Yunqing
    Yi, Nianyu
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2019, 353 : 38 - 48
  • [29] Performance of a new stabilized structure-preserving finite element method for the Allen-Cahn equation
    Manorot, Panason
    Wongsaijai, Ben
    Poochinapan, Kanyuta
    MATHEMATICAL AND COMPUTER MODELLING OF DYNAMICAL SYSTEMS, 2024, 30 (01) : 972 - 1008
  • [30] A fast Galerkin finite element method for a space-time fractional Allen-Cahn equation
    Liu, Huan
    Cheng, Aijie
    Wang, Hong
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2020, 368
12345