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

• DOI: 10.1007/s00607-008-0001-z
• Publication Date: 2008-04-21T06:18:50Z
• Authors: Jian Li; Zhangxin Chen
• Keywords: 0101 mathematics; 01 natural sciences

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.