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| 解Stokes问题的P1非协调四边形元的稳定化方法 | |
| 引用本文： | 黄萍,陈金如.解Stokes问题的P1非协调四边形元的稳定化方法[J].计算数学,2010,32(1):81-96. |
| 作者姓名： | 黄萍 陈金如 |
| 作者单位： | 1. 南京师范大学数学科学学院,南京,210046;中国人民解放军理工大学理学院,南京,211101 2. 南京师范大学数学科学学院,南京,210046 |
| 基金项目： | 国家重点基础研究专项经费，国家自然科学基金，江苏省自然科学基金 |
| 摘 要： | 本文研究了用(~P)_1-Q_0元(其中(~P)_1表示P_1非协调四边形元)解Stokes问题的非协调混合有限元稳定化逼近方法.(~P)_1-Q_0元不满足LBB条件(见7,14] ),因而其不能直接用来求解Stokes问题.受3] 的启发,我们提出了一种用(~P)_1-Q_0元解Stokes问题的稳定化方法,证明了这种方法的稳定性和离散问题解的存在唯一性,得到了最优误差估计.文章最后给出的数值算例验证了我们的理论结果. |
| 关 键 词： | P_1非协调四边形元 Stokes问题 LBB条件 稳定化方法 |
| 收稿时间： | 2008-11-30 |
A STABILIZED METHOD OF P1 NONCONFORMING QUADRILATERAL FINITE ELEMENT FOR SOLVING STOKES PROBLEM |
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| Huang Ping,Chen Jinru.A STABILIZED METHOD OF P1 NONCONFORMING QUADRILATERAL FINITE ELEMENT FOR SOLVING STOKES PROBLEM[J].Mathematica Numerica Sinica,2010,32(1):81-96. | |
| Authors: | Huang Ping Chen Jinru |
| Institution: | 1. School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, China; 2. Institude of Science, PLA University of Science and Technology, Nanjing 211101, China; 3. School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, China |
| Abstract: | In this paper, we study a stabilized method of $\tilde{\textrm P}_1$-Q0 elements (where $\tilde{\textrm P}_1$ denotes P1 nonconforming quadrilateral finite element) approximation of Stokes problem. Since $\tilde{\textrm P}_1$-Q0 elements violate the LBB condition (see 7,14]), they can not be used for solving Stokes problem directly. Motivated by 3], we propose a stabilized method of $\tilde{\textrm P}_1$-Q0 elements for solving Stokes problem. We show the stability, existence and uniqueness of solutions of discrete problem. Meanwhile, an optimal error estimate is obtained. Finally, numerical experiments are presented to confirm our theoretical results. |
| Keywords: | P_1 nonconforming quadrilateral finite element Stokes problem LBB con-dition Stabilized method |
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