三维Stokes方程的一个低阶非协调混合元格式收敛性分析（英文）  

Convergence of a Low Order 3D Nonconforming Mixed Finite Element Scheme for the Stokes Problem

作　　者：任金城[1] 石东洋[2] 

机构地区：[1]商丘师范学院数学与信息科学学院,商丘476000 [2]郑州大学数学系,郑州450052

出　　处：《工程数学学报》2013年第5期781-790,共10页Chinese Journal of Engineering Mathematics

基　　金：The National Natural Science Foundation of China(10971203;11271340);the Research Fund for the Doctoral Program of Higher Education of China(20094101110006);the Youth Development Foundation of Shangqiu Normal University(2010QN013);the JSPS Innovation Program(CXZZ110134)

摘　　要：本文对三维Stokes方程提出一个新的低阶稳定的非协调混合元格式.首先,将该低阶Crouzeix-Raviart型非协调矩形元用于逼近速度空间,压力空间选取分片常数进行逼近,然后得到了关于速度能量模,压力和速度L2-模的最优误差估计.最后,数值算例验证了方法的有效性,并支持了本文的理论分析.In this paper, a new low order stable nonconforming mixed finite element scheme is presented for stationary Stokes problem in three dimensions. We employ the standard formulation of the Stokes problem in the primitive variables and take the new low order Crouzeix-Raviart type nonconforming rectangular element as ap- proximation space for the velocity and piecewise constant elements for the pressure. Optimal error estimate for the approximation of both the velocity and pressure in L^2-norm are obtained, as well as one in broken Hi-norm for the velocity. Numeri- cal examples are presented which demonstrate the effectiveness of the method and coincide with the theoretical analysis.

关 键 词：STOKES方程 非协调混合元格式 INF-SUP条件 最优误差估计 

分 类 号：O242.21[理学—计算数学]