A robust solver for a second order mixed finite element method for the Cahn-Hilliard equation

被引：3
|
作者：
Brenner, Susanne C. [1 ,2 ]
Diegel, Amanda E. [1 ,2 ]
Sung, Li-Yeng [1 ,2 ]
机构：
[1] Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA
[2] Louisiana State Univ, Ctr Computat & Technol, Baton Rouge, LA 70803 USA
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2020年 / 364卷 / 364期
基金：
美国国家科学基金会;
关键词：
Cahn-Hilliard equation; Convex Splitting; Mixed finite element methods; MINRES; Block diagonal preconditioner; Multigrid; ENERGY STABLE SCHEMES; CONVERGENCE; APPROXIMATIONS; STABILITY; MODELS;
D O I：
10.1016/j.cam.2019.06.038
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We develop a robust solver for a second order mixed finite element splitting scheme for the Cahn-Hilliard equation. This work is an extension of our previous work in which we developed a robust solver for a first order mixed finite element splitting scheme for the Cahn-Hilliard equation. The key ingredient of the solver is a preconditioned minimal residual algorithm (with a multigrid preconditioner) whose performance is independent of the spatial mesh size and the time step size for a given interfacial width parameter. The dependence on the interfacial width parameter is also mild. (C) 2019 Elsevier B.V. All rights reserved.
引用
收藏
页数：12
相关论文
共 50 条
  • [31] Stability and Convergence Analysis of Unconditionally Energy Stable and Second Order Method for Cahn-Hilliard Equation
    Yu ZHANG
    Chenhui ZHANG
    Tingfu YAO
    Jun ZHANG
    [J]. Journal of Mathematical Research with Applications, 2023, 43 (06) : 691 - 709
  • [32] A Fully Discrete Mixed Finite Element Method for the Stochastic Cahn-Hilliard Equation with Gradient-Type Multiplicative Noise
    Feng, Xiaobing
    Li, Yukun
    Zhang, Yi
    [J]. JOURNAL OF SCIENTIFIC COMPUTING, 2020, 83 (01)
  • [33] Energy Stable Interior Penalty Discontinuous Galerkin Finite Element Method for Cahn-Hilliard Equation
    Sariaydin-Filibelioglu, Ayse
    Karasozen, Bulent
    Uzunca, Murat
    [J]. INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, 2017, 18 (05) : 303 - 314
  • [34] A Second-order Energy Stable Fourier Spectral Method for the Fractional Cahn-Hilliard Equation
    Mei, Li-quan
    Hou, Yan
    [J]. 2018 INTERNATIONAL CONFERENCE ON COMPUTER, COMMUNICATIONS AND MECHATRONICS ENGINEERING (CCME 2018), 2018, 332 : 724 - 730
  • [35] ON THE CAHN-HILLIARD EQUATION
    ELLIOTT, CM
    ZHENG, SM
    [J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1986, 96 (04) : 339 - 357
  • [36] A Time Splitting Space Spectral Element Method for the Cahn-Hilliard Equation
    Chen, Lizhen
    Xu, Chuanju
    [J]. EAST ASIAN JOURNAL ON APPLIED MATHEMATICS, 2013, 3 (04) : 333 - 351
  • [37] A SECOND ORDER BDF NUMERICAL SCHEME WITH VARIABLE STEPS FOR THE CAHN-HILLIARD EQUATION
    Chen, Wenbin
    Wang, Xiaoming
    Yan, Yue
    Zhang, Zhuying
    [J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2019, 57 (01) : 495 - 525
  • [38] A fully discrete virtual element scheme for the Cahn-Hilliard equation in mixed form
    Liu, Xin
    He, Zhengkang
    Chen, Zhangxin
    [J]. COMPUTER PHYSICS COMMUNICATIONS, 2020, 246
  • [39] ROBUST A POSTERIORI ESTIMATES FOR THE STOCHASTIC CAHN-HILLIARD EQUATION
    Banas, L'ubomir
    Vieth, Christian
    [J]. MATHEMATICS OF COMPUTATION, 2023, 92 (343) : 2025 - 2063
  • [40] Lattice Boltzmann equation method for the Cahn-Hilliard equation
    Zheng, Lin
    Zheng, Song
    Zhai, Qinglan
    [J]. PHYSICAL REVIEW E, 2015, 91 (01):
12345