A Fortin operator for two-dimensional Taylor-Hood elements
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 42 (2008) no. 3, p. 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 : https://doi.org/10.1051/m2an:2008008
Classification:  65N30
Keywords: finite element, Stokes
@article{M2AN_2008__42_3_411_0,
author = {Falk, Richard S.},
title = {A Fortin operator for two-dimensional Taylor-Hood elements},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {42},
number = {3},
year = {2008},
pages = {411-424},
doi = {10.1051/m2an:2008008},
zbl = {1143.65085},
mrnumber = {2423792},
language = {en},
url = {http://www.numdam.org/item/M2AN_2008__42_3_411_0}
}

Falk, Richard S. A Fortin operator for two-dimensional Taylor-Hood elements. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 42 (2008) no. 3, pp. 411-424. doi : 10.1051/m2an:2008008. http://www.numdam.org/item/M2AN_2008__42_3_411_0/

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