Local projection stabilized finite element method for Navier-Stokes equations |
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Authors: | Yan-mei Qin Min-fu Feng Kun Luo Kai-teng Wu |
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Affiliation: | 1. Key Laboratory of Numerical Simulation of Sichuan Province,Neijiang 641112,Sichuan Province,P.R.China;College of Mathematics and Information Science,Neijiang Normal University,Neijiang 641112,Sichuan Province,P.R.China 2. School of Mathematics,Sichuan University,Chengdu 610054,P.R.China |
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Abstract: | This paper extends the results of Matthies, Skrzypacz, and Tubiska for the Oseen problem to the Navier-Stokes problem. For the stationary incompressible NavierStokes 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. |
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Keywords: | local projection Navier-Stokes equations Reynolds number |
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