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基于能量不变二次化法的Cahn-Hilliard方程的数值误差分析

姚廷富 李顺利

姚廷富, 李顺利. 基于能量不变二次化法的Cahn-Hilliard方程的数值误差分析[J]. 华南师范大学学报(自然科学版), 2020, 52(6): 90-96. doi: 10.6054/j.jscnun.2020099
引用本文: 姚廷富, 李顺利. 基于能量不变二次化法的Cahn-Hilliard方程的数值误差分析[J]. 华南师范大学学报(自然科学版), 2020, 52(6): 90-96. doi: 10.6054/j.jscnun.2020099
YAO Tingfu, LI Shunli. An Error Analysis of a Numerical Scheme for the Cahn-Hilliard Equation Based on the Invariant Energy Quadratization Approach[J]. Journal of South China normal University (Natural Science Edition), 2020, 52(6): 90-96. doi: 10.6054/j.jscnun.2020099
Citation: YAO Tingfu, LI Shunli. An Error Analysis of a Numerical Scheme for the Cahn-Hilliard Equation Based on the Invariant Energy Quadratization Approach[J]. Journal of South China normal University (Natural Science Edition), 2020, 52(6): 90-96. doi: 10.6054/j.jscnun.2020099

基于能量不变二次化法的Cahn-Hilliard方程的数值误差分析

doi: 10.6054/j.jscnun.2020099
基金项目: 

国家自然科学基金项目 11761016

贵州省教育厅自然科学研究项目 黔教合KY字[2013]110

贵州省贵阳市科技局贵阳学院专项基金项目 GYU-KYZ[2019-2020]PT06-12

详细信息
    通讯作者:

    姚廷富, 副教授,Email:ytfwdm520@163.com

  • 中图分类号: O241.82

An Error Analysis of a Numerical Scheme for the Cahn-Hilliard Equation Based on the Invariant Energy Quadratization Approach

  • 摘要: 基于能量不变二次化方法,构造了一个求解Cahn-Hilliard方程的线性数值格式,该线性数值格式对非线性项半显式处理,每步迭代相应的半离散化方程只需要求解一个线性方程;证明了该线性数值格式是无条件能量稳定的,而且是唯一可解的;讨论了该线性数值格式在时间方向的误差估计.数值例子表明:该线性数值格式的数值解在时间方向上基本达到二阶精度, 能够有效模拟相位变化过程.
  • 图  1  数值解在t=1与t=2时刻的相位图

    Figure  1.  The phase diagram of the numerical results on t=1 and t=2

    表  1  能量不变二次化法的Cahn-Hilliard方程的数值结果

    Table  1.   The numerical results of invariant energy quadratization approach of Cahn-Hilliard equation

    δt L2范数下的误差
    0.01 0.008 235
    0.005 0.005 224 1.651 101
    0.002 5 0.002 406 1.752 124
    0.001 25 0.001 126 1.861 113
    0.000 625 0.000 722 1.924 021
    0.000 312 5 0.000 465 1.945 233
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-03-24
  • 刊出日期:  2020-12-25

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