A Fortin operator for two-dimensional Taylor-Hood elements

Richard S. Falk

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

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

Abstract

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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.

How to cite

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Falk, 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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  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.  
  3. D. Boffi, Three-dimensional finite element methods for the Stokes problem. SIAM J. Numer. Anal.34 (1997) 664–670.  
  4. F. Brezzi and R.S. Falk, Stability of higher-order Hood-Taylor methods. SIAM J. Numer. Anal.28 (1991) 581–590.  
  5. F. Brezzi and M. Fortin, Mixed and hybrid finite element methods. Springer-Verlag, New York (1991).  
  6. 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).  
  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.  
  8. R. Stenberg, Error analysis of some finite element methods for the Stokes problem. Math. Comp.54 (1990) 494–548.  
  9. 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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