CAJ | 학술논문

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.
본문연구료용(~P)_1-Q_0원(기중(~P)_1표시P_1비협조사변형원)해Stokes문제적비협조혼합유한원은정화핍근방법.(~P)_1-Q_0원불만족LBB조건(견[7,14] ),인이기불능직접용래구해Stokes문제.수[3] 적계발,아문제출료일충용(~P)_1-Q_0원해Stokes문제적은정화방법,증명료저충방법적은정성화리산문제해적존재유일성,득도료최우오차고계.문장최후급출적수치산례험증료아문적이론결과.
In this paper, we study a stabilized method of (~P)_1-Q_0 elements (where (~P)_1 denotes P_1 nonconforming quadrilateral finite element) approximation of Stokes problem. Since (~P)_1-Q_0 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 (~P)_1-Q_0 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.