# A Fortin operator for two-dimensional Taylor-Hood elements

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

- Volume: 42, Issue: 3, page 411-424
- ISSN: 0764-583X

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topFalk, Richard S.. "A Fortin operator for two-dimensional Taylor-Hood elements." ESAIM: Mathematical Modelling and Numerical Analysis 42.3 (2008): 411-424. <http://eudml.org/doc/250343>.

@article{Falk2008,

abstract = {
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.
},

author = {Falk, Richard S.},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Finite element; Stokes.; finite element},

language = {eng},

month = {4},

number = {3},

pages = {411-424},

publisher = {EDP Sciences},

title = {A Fortin operator for two-dimensional Taylor-Hood elements},

url = {http://eudml.org/doc/250343},

volume = {42},

year = {2008},

}

TY - JOUR

AU - Falk, Richard S.

TI - A Fortin operator for two-dimensional Taylor-Hood elements

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2008/4//

PB - EDP Sciences

VL - 42

IS - 3

SP - 411

EP - 424

AB -
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.

LA - eng

KW - Finite element; Stokes.; finite element

UR - http://eudml.org/doc/250343

ER -

## References

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- F. Brezzi and M. Fortin, Mixed and hybrid finite element methods. Springer-Verlag, New York (1991).
- V. Girault and P.-A. Raviart, Finite Element Methods for Navier-Stokes equations: theory and algorithms, Springer Series in Computational Mathematics5. Springer-Verlag, Berlin (1986).
- 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.
- R. Stenberg, Error analysis of some finite element methods for the Stokes problem. Math. Comp.54 (1990) 494–548.
- R. Verfürth, Error estimates for a mixed finite element approximation of the Stokes equations. RAIRO Anal. Numér.18 (1984) 175–182.

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