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Performance of several stabilized finite element methods for the Stokes equations based on the lowest equal-order pairs

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Abstract

In this paper the performance of various stabilized mixed finite element methods based on the lowest equal-order polynomial pairs (i.e., P 1 − P 1 or Q 1 − Q 1) are numerically investigated for the stationary Stokes equations: penalty, regular, multiscale enrichment, and local Gauss integration methods. Comparisons between them will be carried out in terms of the critical factors: stabilization parameters, convergence rates, consistence, and mesh effects. It is numerically drawn that the local Gauss integration method is a favorite method among these methods.

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Authors and Affiliations

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

    Jian Li

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

    Jian Li, Yinnian He & Zhangxin Chen

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

    Jian Li & Zhangxin Chen

Authors
  1. Jian Li
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  2. Yinnian He
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  3. Zhangxin Chen
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Corresponding author

Correspondence to Jian Li.

Additional information

Communicated by W. Hackbusch.

This research was subsidized by the NSF of China 10701001, 10671154, the National Basic Research Program (No. 2005CB321703), and the Natural Science Basic Research Plan in Shaanxi Province of China (No. SJ08A14) and by the US National Science Foundation grant DMS-0609995 and CMG Chair Funds in Reservoir Simulation.

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Li, J., He, Y. & Chen, Z. Performance of several stabilized finite element methods for the Stokes equations based on the lowest equal-order pairs. Computing 86, 37–51 (2009). https://doi.org/10.1007/s00607-009-0064-5

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  • DOI: https://doi.org/10.1007/s00607-009-0064-5

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