A new second order nonconforming mixed finite element scheme for the stationary Stokes and Navier-Stokes equations

作者：Shi Dongyang^*; Ren Jincheng; Hao Xiaobin

来源：Applied Mathematics and Computation, 2009, 207(2): 462-477.

DOI：10.1016/j.amc.2008.10.058

• Stationary Stokes and Navier-Stokes equations
• Nonconforming mixed finite element scheme
• Optimal error estimates

In this paper, a new stable nonconforming mixed finite element scheme with second order accuracy is proposed for the stationary Stokes and Navier-Stokes equations, in which, a new nonconforming rectangular element is taken for approximating space the velocity and the bilinear element for the pressure. The optimal error estimates for the approximation of both the velocity and the pressure in L(2)-norm are established, as well as one in a broken H(1)-norm for the velocity. Numerical experiments are given which are consistent with our theoretical analysis.

• 出版日期2009-1-15
• 单位河南工程学院; 商丘师范学院; 郑州大学