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Applied Mathematics and Mechanics

, Volume 31, Issue 5, pp 651–664 | Cite as

Local projection stabilized finite element method for Navier-Stokes equations

  • Yan-mei Qin (覃燕梅)
  • Min-fu Feng (冯民富)Email author
  • Kun Luo (罗 鲲)
  • Kai-teng Wu (吴开滕)
Article

Abstract

This paper extends the results of Matthies, Skrzypacz, and Tubiska for the Oseen problem to the Navier-Stokes problem. For the stationary incompressible Navier-Stokes equations, a local projection stabilized finite element scheme is proposed. The scheme overcomes convection domination and improves the restrictive inf-sup condition. It not only is a two-level approach but also is adaptive for pairs of spaces defined on the same mesh. Using the approximation and projection spaces defined on the same mesh, the scheme leads to much more compact stencils than other two-level approaches. On the same mesh, besides the class of local projection stabilization by enriching the approximation spaces, two new classes of local projection stabilization of the approximation spaces are derived, which do not need to be enriched by bubble functions. Based on a special interpolation, the stability and optimal prior error estimates are shown. Numerical results agree with some benchmark solutions and theoretical analysis very well.

Key words

local projection Navier-Stokes equations Reynolds number 

Chinese Library Classification

O242.21 

2000 Mathematics Subject Classification

65N30 76D05 

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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Yan-mei Qin (覃燕梅)
    • 1
    • 2
  • Min-fu Feng (冯民富)
    • 3
    Email author
  • Kun Luo (罗 鲲)
    • 3
  • Kai-teng Wu (吴开滕)
    • 1
    • 2
  1. 1.Key Laboratory of Numerical Simulation of Sichuan ProvinceNeijiangSichuan Province, P. R. China
  2. 2.College of Mathematics and Information ScienceNeijiang Normal UniversityNeijiangSichuan Province, P. R. China
  3. 3.School of MathematicsSichuan UniversityChengduP. R. China

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