A STABILIZED METHOD OF P1 NONCONFORMING QUADRILATERAL FINITE ELEMENT FOR SOLVING STOKES PROBLEM
解Stokes问题的P1非协调四边形元的稳定化方法

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.