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Stabilized finite element method for the stationary Navier-Stokes equations. (English) Zbl 1069.76031
Summary: We investigate a stabilized finite element method for two-dimensional stationary incompressible Navier-Stokes equations. A macroelement condition is introduced for constructing the local stabilized formulation of the stationary Navier-Stokes equations. By satisfying this condition, the stability of ${Q}_{1}-{P}_{0}$ quadrilateral element and ${P}_{1}-{P}_{0}$ triangular element are established. Moreover, the well-posedness and optimal error estimates of the stabilized finite element method for stationary Navier-Stokes equations are obtained. Finally, some numerical tests confirm the theoretical results of the stabilized finite element method.
##### MSC:
 76M10 Finite element methods (fluid mechanics) 76D05 Navier-Stokes equations (fluid dynamics) 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE) 65N35 Spectral, collocation and related methods (BVP of PDE)
##### References:
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