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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:
35Q30Stokes and Navier-Stokes equations
76M12Finite volume methods (fluid mechanics)
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
76D05Navier-Stokes equations (fluid dynamics)