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A new stabilized finite volume method for the stationary Stokes equations

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Abstract

In this paper we develop and study a new stabilized finite volume method for the two-dimensional Stokes equations. This method is based on a local Gauss integration technique and the conforming elements of the lowest-equal order pair (i.e., the P 1–P 1 pair). After a relationship between this method and a stabilized finite element method is established, an error estimate of optimal order in the H 1-norm for velocity and an estimate in the L 2-norm for pressure are obtained. An optimal error estimate in the L 2-norm for the velocity is derived under an additional assumption on the body force.

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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 and Petroleum Engineering, Schulich School of Engineering, University of Calgary, 2500 University Drive N.W. Calgary, Alberta, 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 Zhangxin Chen.

Additional information

Communicated by: Jinchao Xu.

This work is supported in part by the NSF of China 10701001 and by the US National Science Foundation grant DMS-0609995 and CMG Chair Funds in Reservoir Simulation.

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Li, J., Chen, Z. A new stabilized finite volume method for the stationary Stokes equations. Adv Comput Math 30, 141–152 (2009). https://doi.org/10.1007/s10444-007-9060-5

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  • DOI: https://doi.org/10.1007/s10444-007-9060-5

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