A new local stabilized nonconforming finite element method for the Stokes equations

Authors:
Jian Li;Zhangxin Chen
Affiliations:
Baoji Univ. of Arts and Sci., Dept. of Math., 721007, Baoji, PRC and Xi’an Jiaotong University, Faculty of Science, Xi’an, 710049, People’s Republic of China;Univ. of Calgary, Dept. of Chemical & Petroleum Eng., Schulich Sch. of Eng., 2500 Univ. Drive N.W. Calgary, T2N 1N4, Calgary, AB, Canada and Xi’’an Jiaotong Univ., Fac. of Sci., Xi&# ...
Venue:
Computing
Year:
2008

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Abstract

In this paper, we propose and study a new local stabilized nonconforming finite method based on two local Gauss integrations for the two-dimensional Stokes equations. The nonconforming method uses the lowest equal-order pair of mixed finite elements (i.e., NCP 1–P 1). After a stability condition is shown for this stabilized method, its optimal-order error estimates are obtained. In addition, numerical experiments to confirm the theoretical results are presented. Compared with some classical, closely related mixed finite element pairs, the results of the present NCP 1–P 1 mixed finite element pair show its better performance than others.