三维Stokes方程的一个低阶非协调混合元格式收敛性分析

摘要

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 L2-norm are obtained, as well as one in broken H 1-norm for the velocity. Numeri-cal examples are presented which demonstrate the effectiveness of the method and coincide with the theoretical analysis.%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。