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具有滑动边界条件Stokes问题的自适应Uzawa块松弛算法

张茂林 冉静 张守贵

张茂林, 冉静, 张守贵. 具有滑动边界条件Stokes问题的自适应Uzawa块松弛算法[J]. 应用数学和力学, 2021, 42(2): 188-198. doi: 10.21656/1000-0887.410170
引用本文: 张茂林, 冉静, 张守贵. 具有滑动边界条件Stokes问题的自适应Uzawa块松弛算法[J]. 应用数学和力学, 2021, 42(2): 188-198. doi: 10.21656/1000-0887.410170
ZHANG Maolin, RAN Jing, ZHANG Shougui. A Self-Adaptive Uzawa Block Relaxation Method for Stokes Problems With Slip Boundary Conditions[J]. Applied Mathematics and Mechanics, 2021, 42(2): 188-198. doi: 10.21656/1000-0887.410170
Citation: ZHANG Maolin, RAN Jing, ZHANG Shougui. A Self-Adaptive Uzawa Block Relaxation Method for Stokes Problems With Slip Boundary Conditions[J]. Applied Mathematics and Mechanics, 2021, 42(2): 188-198. doi: 10.21656/1000-0887.410170

具有滑动边界条件Stokes问题的自适应Uzawa块松弛算法

doi: 10.21656/1000-0887.410170
基金项目: 国家自然科学基金(11971085);重庆市自然科学基金(cstc2020jcyjmsxmX0066);重庆市高校创新研究群体项目(CXQT19018);重庆市研究生教育优质课程项目(201949)
详细信息
    作者简介:

    张茂林(1995—), 女, 硕士生(E-mail: 674003207@qq.com);张守贵(1973—), 男, 教授, 博士, 硕士生导师(通讯作者. E-mail: shgzhnag@cqnu.edu.cn).

  • 中图分类号: O221.6

A Self-Adaptive Uzawa Block Relaxation Method for Stokes Problems With Slip Boundary Conditions

Funds: The National Natural Science Foundation of China(11971085)
  • 摘要: 对一类具有非线性滑动边界条件的Stokes问题,得到了求其数值解的自适应Uzawa块松弛算法(SUBRM).通过该问题导出的变分问题,引入辅助变量将原问题转化为一个基于增广Lagrange函数表示的鞍点问题,并采用Uzawa块松弛算法(UBRM)求解.为了提高算法性能,提出利用迭代函数自动选取合适罚参数的自适应法则.该算法的优点是每次迭代只需计算一个线性问题,同时显式计算辅助变量.对算法的收敛性进行了理论分析,最后用数值结果验证了该算法的可行性和有效性.
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出版历程
  • 收稿日期:  2020-06-11
  • 修回日期:  2020-07-25
  • 刊出日期:  2021-02-01

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