no. 3
A Fortin operator for two-dimensional Taylor-Hood elements
ESAIM: Modélisation mathématique et analyse numérique, Tome 42 (2008) no. 3, pp. 411-424

A standard method for proving the inf-sup condition implying stability of finite element approximations for the stationary Stokes equations is to construct a Fortin operator. In this paper, we show how this can be done for two-dimensional triangular and rectangular Taylor-Hood methods, which use continuous piecewise polynomial approximations for both velocity and pressure.

DOI : 10.1051/m2an:2008008
Classification : 65N30
Keywords: finite element, Stokes 
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     title = {A {Fortin} operator for two-dimensional {Taylor-Hood} elements},
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Falk, Richard S. A Fortin operator for two-dimensional Taylor-Hood elements. ESAIM: Modélisation mathématique et analyse numérique, Tome 42 (2008) no. 3, pp. 411-424. doi: 10.1051/m2an:2008008

[1] M. Bercovier and O. Pironneau, Error estimates for finite element solution of the Stokes problem in the primitive variables. Numer. Math. 33 (1979) 211-224. | Zbl | MR

[2] D. Boffi, Stability of higher-order triangular Hood-Taylor methods for the stationary Stokes equation. Math. Models Methods Appl. Sci. 4 (1994) 223-235. | Zbl | MR

[3] D. Boffi, Three-dimensional finite element methods for the Stokes problem. SIAM J. Numer. Anal. 34 (1997) 664-670. | Zbl | MR

[4] F. Brezzi and R.S. Falk, Stability of higher-order Hood-Taylor methods. SIAM J. Numer. Anal. 28 (1991) 581-590. | Zbl | MR

[5] F. Brezzi and M. Fortin, Mixed and hybrid finite element methods. Springer-Verlag, New York (1991). | Zbl | MR

[6] V. Girault and P.-A. Raviart, Finite Element Methods for Navier-Stokes equations: theory and algorithms, Springer Series in Computational Mathematics 5. Springer-Verlag, Berlin (1986). | Zbl | MR

[7] L.R. Scott and M. Vogelius, Norm estimates for a maximal right inverse of the divergence operator in spaces of piecewise polynomials. RAIRO Modél. Math. Anal. Numér. 19 (1985) 111-143. | Zbl | MR | Numdam

[8] R. Stenberg, Error analysis of some finite element methods for the Stokes problem. Math. Comp. 54 (1990) 494-548. | Zbl | MR

[9] R. Verfürth, Error estimates for a mixed finite element approximation of the Stokes equations. RAIRO Anal. Numér. 18 (1984) 175-182. | Zbl | MR | Numdam

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