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The finite volume method based on stabilized finite element for the stationary Navier-Stokes problem. (English) Zbl 1117.35061
Summary: A finite volume method (FVM) based on stabilized finite element approximation for the two-dimensional stationary Navier-Stokes equations is investigated. A macroelement condition is introduced. We obtain the well-posedness of the FVM. Moreover, for the quadrilateral and triangular partitions, an optimal ${H}^{1}$ error estimate of the finite volume solution ${u}_{h}$ and ${L}^{2}$ error estimate for ${p}_{h}$ are found. Finally, we provide a numerical example.
##### MSC:
 35Q30 Stokes and Navier-Stokes equations 76M12 Finite volume methods (fluid mechanics) 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE) 76D05 Navier-Stokes equations (fluid dynamics)