Efficient linear and unconditionally energy stable schemes for the modified phase field crystal equation

被引：0
|
作者：
Xiaoli Li [1 ]
Jie Shen [2 ]
机构：
[1] School of Mathematics, Shandong University
[2] Department of Mathematics, Purdue University
来源：
ScienceChina(Mathematics) | 2022年 / 65卷 / 10期
基金：
美国国家科学基金会; 中国国家自然科学基金;
关键词：
D O I：
暂无
中图分类号：
O175 [微分方程、积分方程];
学科分类号：
070104 ;
摘要：
In this paper, we construct efficient schemes based on the scalar auxiliary variable block-centered finite difference method for the modified phase field crystal equation, which is a sixth-order nonlinear damped wave equation. The schemes are linear, conserve mass and unconditionally dissipate a pseudo energy. We prove rigorously second-order error estimates in both time and space for the phase field variable in discrete norms. We also present some numerical experiments to verify our theoretical results and demonstrate the robustness and accuracy.
引用
收藏
页码：2201 / 2218
页数：18
相关论文
共 50 条
  • [1] Efficient linear and unconditionally energy stable schemes for the modified phase field crystal equation
    Li, Xiaoli
    Shen, Jie
    SCIENCE CHINA-MATHEMATICS, 2022, 65 (10) : 2201 - 2218
  • [2] Efficient linear and unconditionally energy stable schemes for the modified phase field crystal equation
    Xiaoli Li
    Jie Shen
    Science China Mathematics, 2022, 65 : 2201 - 2218
  • [3] Linear and unconditionally energy stable schemes for the modified phase field crystal equation
    Liang, Yihong
    Jia, Hongen
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2024, 153 : 197 - 212
  • [4] Efficient and unconditionally energy stable exponential-SAV schemes for the phase field crystal equation
    Zhang, Fan
    Sun, Hai -Wei
    Sun, Tao
    APPLIED MATHEMATICS AND COMPUTATION, 2024, 470
  • [5] An unconditionally energy-stable method for the phase field crystal equation
    Gomez, Hector
    Nogueira, Xesus
    COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2012, 249 : 52 - 61
  • [6] Efficient unconditionally stable numerical schemes for a modified phase field crystal model with a strong nonlinear vacancy potential
    Pei, Shuaichao
    Hou, Yanren
    Yan, Wenjing
    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2022, 38 (01) : 65 - 101
  • [7] Energy stable and efficient finite-difference nonlinear multigrid schemes for the modified phase field crystal equation
    Baskaran, Arvind
    Hu, Zhengzheng
    Lowengrub, John S.
    Wang, Cheng
    Wise, Steven M.
    Zhou, Peng
    JOURNAL OF COMPUTATIONAL PHYSICS, 2013, 250 : 270 - 292
  • [8] ENERGY STABLE AND CONVERGENT FINITE ELEMENT SCHEMES FOR THE MODIFIED PHASE FIELD CRYSTAL EQUATION
    Grasselli, Maurizio
    Pierre, Morgan
    ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2016, 50 (05): : 1523 - 1560
  • [9] A second-order linear unconditionally energy-stable scheme for the phase field crystal equation
    Li, Yaoda
    Li, Min
    Zho, Boya
    Han, Zhibin
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2025, 455
  • [10] Novel linear decoupled and unconditionally energy stable numerical methods for the modified phase field crystal model
    Liu, Zhengguang
    Chen, Shuangshuang
    APPLIED NUMERICAL MATHEMATICS, 2021, 163 : 1 - 14
12345