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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.
@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 },
pages = {411--424},
publisher = {EDP-Sciences},
volume = {42},
number = {3},
year = {2008},
doi = {10.1051/m2an:2008008},
mrnumber = {2423792},
zbl = {1143.65085},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2008008/}
}
TY - JOUR AU - Falk, Richard S. TI - A Fortin operator for two-dimensional Taylor-Hood elements JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2008 SP - 411 EP - 424 VL - 42 IS - 3 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an:2008008/ DO - 10.1051/m2an:2008008 LA - en ID - M2AN_2008__42_3_411_0 ER -
%0 Journal Article %A Falk, Richard S. %T A Fortin operator for two-dimensional Taylor-Hood elements %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2008 %P 411-424 %V 42 %N 3 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an:2008008/ %R 10.1051/m2an:2008008 %G en %F M2AN_2008__42_3_411_0
Falk, Richard S. A Fortin operator for two-dimensional Taylor-Hood elements. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 42 (2008) no. 3, pp. 411-424. doi: 10.1051/m2an:2008008
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