Error analysis of first- and second-order linear, unconditionally energy-stable schemes for the Swift-Hohenberg equation

被引：3
|
作者：
Qi, Longzhao [1 ]
Hou, Yanren [1 ]
机构：
[1] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Peoples R China
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2022年 / 127卷
基金：
中国国家自然科学基金;
关键词：
Swift-Hohenberg equation; Invariant energy quadratization (IEQ) scheme; Energy stability; Error analysis; PHASE-FIELD MODEL; NUMERICAL APPROXIMATIONS; ADDITIVE NOISE; NEURAL FIELDS; DYNAMICS; CAHN;
D O I：
10.1016/j.camwa.2022.10.007
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this work, we present first-and second-order energy-stable linear schemes for the Swift-Hohenberg equation based on first-order backward Euler and Crank-Nicolson schemes, respectively. We prove rigorously that the schemes satisfy the energy dissipation property. We also derive the error analysis for our schemes. Moreover, we adopt a spectral-Galerkin approximation for the spatial variables and establish error estimates for the fully discrete second-order Crank-Nicolson scheme. Numerical results are presented to validate our theoretical analysis.
引用
收藏
页码：192 / 212
页数：21
相关论文
共 50 条
  • [41] Linear, second-order, unconditionally energy stable scheme for an electrohydrodynamic model with variable density and conductivity
    Pan, Mingyang
    Fu, Chengxing
    Zhu, Wenxing
    Jiao, Fengyu
    He, Dongdong
    [J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2023, 125
  • [42] Unconditionally energy stable second-order numerical schemes for the Functionalized Cahn-Hilliard gradient flow equation based on the SAV approach
    Zhang, Chenhui
    Ouyang, Jie
    [J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2021, 84 : 16 - 38
  • [43] SECOND ORDER, LINEAR, AND UNCONDITIONALLY ENERGY STABLE SCHEMES FOR A HYDRODYNAMIC MODEL OF SMECTIC-A LIQUID CRYSTALS
    Chen, Rui
    Yang, Xiaofeng
    Zhang, Hui
    [J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2017, 39 (06): : A2808 - A2833
  • [44] First- and second-order error estimates in Monte Carlo integration
    Bakx, R.
    Kleiss, R. H. P.
    Versteegen, F.
    [J]. COMPUTER PHYSICS COMMUNICATIONS, 2016, 208 : 29 - 34
  • [45] Second-Order SAV Schemes for the Nonlinear Schrödinger Equation and Their Error Analysis
    Beichuan Deng
    Jie Shen
    Qingqu Zhuang
    [J]. Journal of Scientific Computing, 2021, 88
  • [46] First and second order unconditionally energy stable schemes for topology optimization based on phase field method
    Yu, Qian
    Wang, Kunyang
    Xia, Binhu
    Li, Yibao
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2021, 405
  • [47] A second-order accurate and unconditionally energy stable numerical scheme for nonlinear sine-Gordon equation
    Zhang, Jun
    Zhang, Hui
    Cao, Junying
    Chen, Hu
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2024, 537 (02)
  • [48] Unconditionally energy stable second-order numerical scheme for the Allen–Cahn equation with a high-order polynomial free energy
    Junseok Kim
    Hyun Geun Lee
    [J]. Advances in Difference Equations, 2021
  • [49] Unconditionally strong energy stable scheme for Cahn-Hilliard equation with second-order temporal accuracy
    Lee, Seunggyu
    [J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2023, 46 (06) : 6463 - 6469
  • [50] Iterative analysis of non-linear Swift-Hohenberg equations under nonsingular fractional order derivative
    Ahmad, Israr
    Abdeljawad, Thabet
    Mahariq, Ibrahim
    Shah, Kamal
    Mlaiki, Nabil
    Rahman, Ghaus Ur
    [J]. RESULTS IN PHYSICS, 2021, 23
12345