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Zbl 1117.35061
He, Guoliang; He, Yinnian
The finite volume method based on stabilized finite element for the stationary Navier-Stokes problem. (English)
[J] J. Comput. Appl. Math. 205, No. 1, 651-665 (2007). ISSN 0377-0427

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 2000:: *35Q30 Stokes and Navier-Stokes equations
76M12 Finite volume methods
65N30 Finite numerical methods (BVP of PDE)
76D05 Navier-Stokes equations (fluid dynamics)

Keywords: finite volume method; stabilized finite element approximation; error estimation

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Zentralblatt MATH Berlin [Germany]