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A stabilized finite volume method for Stokes equations using the lowest order P 1 − P 0 element pair

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Abstract

We present a new stabilized finite volume method for Stokes problem using the lowest order P 1 − P 0 element pair. To offset the lack of the inf -sup condition, a simple jump term of discrete pressure is added to the continuity approximation equation. A discrete inf -sup condition is established for this stabilized scheme. The optimal error estimates are given in the H 1- and L 2-norms for velocity and in the L 2-norm for pressure, respectively.

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Authors and Affiliations

  1. Department of Mathematics and the State Key Laboratory of SAPI, Research Center of National Metallurgical Automation, Northeastern University, Shenyang, 110004, China

    Tie Zhang

  2. The State Key Laboratory of Synthetical Automation for Process Industries, Research Center of National Metallurgical Automation, Northeastern University, Shenyang, 110004, China

    Lixin Tang

Authors
  1. Tie Zhang
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  2. Lixin Tang
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Correspondence to Tie Zhang.

Additional information

Communicated by: Charlie Elliott

This work was supported by the National Natural Science Funds of China, No. 11371081; and the State Key Laboratory of SAPI Fundamental Research Funds, No. 2013ZCX02.

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Zhang, T., Tang, L. A stabilized finite volume method for Stokes equations using the lowest order P 1 − P 0 element pair. Adv Comput Math 41, 781–798 (2015). https://doi.org/10.1007/s10444-014-9385-9

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  • DOI: https://doi.org/10.1007/s10444-014-9385-9

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