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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Baoji University of Arts and Sciences, Baoji, 721007, People’s Republic of China

    Jian Li

  2. Department of Chemical & Petroleum Engineering, Schulich School of Engineering, University of Calgary, 2500 University Drive N.W. Calgary, Calgary, AB, T2N 1N4, Canada

    Zhangxin Chen

  3. Faculty of Science, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Jian Li & Zhangxin Chen

Authors
  1. Jian Li
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  2. Zhangxin Chen
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Correspondence to Jian Li.

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Li, J., Chen, Z. A new local stabilized nonconforming finite element method for the Stokes equations. Computing 82, 157–170 (2008). https://doi.org/10.1007/s00607-008-0001-z

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  • DOI: https://doi.org/10.1007/s00607-008-0001-z

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