Hostname: page-component-74656f9884-2dmjx Total loading time: 0 Render date: 2026-11-10T07:09:54.875Z Has data issue: false hasContentIssue false
  • English
  • Français

A Fortin operator for two-dimensionalTaylor-Hood elements

Published online by Cambridge University Press:  03 April 2008

Richard S. Falk
Richard S. Falk*
Affiliation:
Department of Mathematics, Rutgers University, Piscataway, NJ 08854-8019, USA. falk@math.rutgers.edu
Get access

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.

Keywords

Finite elementStokes.

Information

Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 42 , Issue 3 , May 2008 , pp. 411 - 424
Copyright
© EDP Sciences, SMAI, 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Bercovier, M. and Pironneau, O., Error estimates for finite element solution of the Stokes problem in the primitive variables. Numer. Math. 33 (1979) 211–224. CrossRef
Boffi, D., Stability of higher-order triangular Hood-Taylor methods for the stationary Stokes equation. Math. Models Methods Appl. Sci. 4 (1994) 223–235. CrossRef
Boffi, D., Three-dimensional finite element methods for the Stokes problem. SIAM J. Numer. Anal. 34 (1997) 664–670. CrossRef
Brezzi, F. and Falk, R.S., Stability of higher-order Hood-Taylor methods. SIAM J. Numer. Anal. 28 (1991) 581–590. CrossRef
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 Mathematics 5. Springer-Verlag, Berlin (1986).
Scott, L.R. and Vogelius, M., 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. CrossRef
Stenberg, R., Error analysis of some finite element methods for the Stokes problem. Math. Comp. 54 (1990) 494–548. CrossRef
Verfürth, R., Error estimates for a mixed finite element approximation of the Stokes equations. RAIRO Anal. Numér. 18 (1984) 175–182. CrossRef