• 论文 •

求解定常不可压Stokes方程的两层罚函数方法

1. 1. 河南理工大学数学与信息科学学院, 焦作 454003;
2. 杭州电子科技大学理学院, 杭州 310027
• 收稿日期:2017-09-02 出版日期:2019-09-15 发布日期:2019-08-21
• 通讯作者: 李世顺,Email:lss6@sina.com
• 基金资助:

国家自然科学基金项目（No.11401177，11701133），浙江省教育厅科研项目（No.Y201533698）.

Li Shishun, Qi FenFen, Shao Xinping. TWO-LEVEL PENALTY METHOD FOR THE STEADY INCOMPRESSIBLE STOKES EQUATIONS[J]. Mathematica Numerica Sinica, 2019, 41(3): 259-265.

TWO-LEVEL PENALTY METHOD FOR THE STEADY INCOMPRESSIBLE STOKES EQUATIONS

Li Shishun1, Qi FenFen1, Shao Xinping2

1. 1. School of Mathematics & Information Science, Henan Polytechnic University, Jiaozuo 454003, China;
2. School of Science & Hangzhou Dianzi University, Hangzhou 310027, China
• Received:2017-09-02 Online:2019-09-15 Published:2019-08-21

In this paper, we present a two-level penalty method for the steady incompressible Stokes equations by employing two finite element spaces. This method involves solving one small Stokes equation on the coarse space and two penalty equations on the fine space (the linear systems with same symetric and positive coefficient matrices). The convergence shows that the coarse space can be chosen very small. Moreover, the penalty parameter is only dependent on the coarse mesh size and the regularity of the problem. Therefore, the resulting solution still achieves asymptotically optimal accuracy when the penalty parameter is chosen "not very small". The numerical results confirm the convergence analysis, and the numerical comparison also shows that this method is efficient for solving the steady incompressible Stokes equations.

MR(2010)主题分类:

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