解Stokes问题的P_1非协调四边形元的稳定化方法

A STABILIZED METHOD OF P_1 NONCONFORMING QUADRILATERAL FINITE ELEMENT FOR SOLVING STOKES PROBLEM

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.

In this paper,we study a stabilized method of P1-Qo elements（where P1 denotes P1 nonconforming quadrilateral finite element） approximation of Stokes problem.Since P1-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 P1-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.