A Nonconforming Anisotropic Finite Element Approximation With Moving Grids For Stokes Problem
Dong-yang Shi 1, Yi-ran Zhang 21 Department of Mathematics, Zhengzhou University, Zhengzhou 450052, China
2 School of Mathematical Science, Peking University, Beijing 100871, China
Received 2004-2-17 Revised 2005-12-7 Online 2006-9-14 Accepted
This paper is devoted to the five parameters nonconforming finite element schemes with moving grids for velocity-pressure mixed formulations of the nonstationary Stokes problem in 2-D. We show that this element has anisotropic behavior and derive anisotropic error estimations in some certain norms of the velocity and the pressure based on some novel techniques. Especially through careful analysis we get an interesting result on consistency error estimation, which has never been seen for mixed finite element methods in the previously literatures.
Key words: Stokes problem; Nonconforming finite element; Anisotropy; Moving grids; Error estimate.