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A stabilized finite element method based on local polynomial pressure projection for the stationary Navier-Stokes equations. (English) Zbl 1155.35406
Summary: This article considers a stabilized finite element approximation for the branch of nonsingular solutions of the stationary Navier-Stokes equations based on local polynomial pressure projection by using the lowest equal-order elements. The proposed stabilized method has a number of attractive computational properties. Firstly, it is free from stabilization parameters. Secondly, it only requires the simple and efficient calculation of Gauss integral residual terms. Thirdly, it can be implemented at the element level. The optimal error estimate is obtained by the standard finite element technique. Finally, comparison with other methods, through a series of numerical experiments, shows that this method has better stability and accuracy.

35Q30 Navier-Stokes equations
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
76M10 Finite element methods applied to problems in fluid mechanics
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