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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:
76M10Finite element methods (fluid mechanics)
76D05Navier-Stokes equations (fluid dynamics)
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
65N35Spectral, collocation and related methods (BVP of PDE)
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