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New nonconforming finite element method for solving transient Naiver-Stokes equations

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Abstract

For transient Naiver-Stokes problems, a stabilized nonconforming finite element method is presented, focusing on two pairs inf-sup unstable finite element spaces, i.e., P NC1 /P NC1 triangular and P NQ1 /P NQ1 quadrilateral finite element spaces. The semiand full-discrete schemes of the stabilized method are studied based on the pressure projection and a variational multi-scale method. It has some attractive features: avoiding higher-order derivatives and edge-based data structures, adding a discrete velocity term only on the fine scale, being effective for high Reynolds number fluid flows, and avoiding increased computation cost. For the full-discrete scheme, it has second-order estimations of time and is unconditionally stable. The presented numerical results agree well with the theoretical results.

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Authors and Affiliations

  1. School of Mathematics Sciences, University of Electronic Science and Technology of China, Chengdu, 610054, P. R. China

    Chun-mei Xie  (谢春梅)

  2. School of Mathematics, Sichuan University, Chengdu, 610064, P. R. China

    Min-fu Feng  (冯民富)

Authors
  1. Chun-mei Xie  (谢春梅)
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  2. Min-fu Feng  (冯民富)
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Correspondence to Min-fu Feng  (冯民富).

Additional information

Project supported by the National Natural Science Foundation of China (No. 11271273)

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Xie, Cm., Feng, Mf. New nonconforming finite element method for solving transient Naiver-Stokes equations. Appl. Math. Mech.-Engl. Ed. 35, 237–258 (2014). https://doi.org/10.1007/s10483-014-1787-6

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  • DOI: https://doi.org/10.1007/s10483-014-1787-6

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2010 Mathematics Subject Classification

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