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We introduce a new stable MINI-element pair for incompressible Stokes equations on quadrilateral meshes, which uses the smallest number of bubbles for the velocity. The pressure is discretized with the P1-midpoint-edge-continuous elements and each component of the velocity field is done with the standard Q1-conforming elements enriched by one bubble a quadrilateral. The superconvergence in the pressure of the proposed pair is analyzed on uniform rectangular meshes, and tested numerically on uniform and non-uniform meshes.
@article{M2AN_2014__48_4_955_0,
author = {Kwon, Oh-In and Park, Chunjae},
title = {A new quadrilateral {MINI-element} for {Stokes} equations},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {955--968},
publisher = {EDP-Sciences},
volume = {48},
number = {4},
year = {2014},
doi = {10.1051/m2an/2013129},
mrnumber = {3264342},
zbl = {1299.76140},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013129/}
}
TY - JOUR AU - Kwon, Oh-In AU - Park, Chunjae TI - A new quadrilateral MINI-element for Stokes equations JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2014 SP - 955 EP - 968 VL - 48 IS - 4 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013129/ DO - 10.1051/m2an/2013129 LA - en ID - M2AN_2014__48_4_955_0 ER -
%0 Journal Article %A Kwon, Oh-In %A Park, Chunjae %T A new quadrilateral MINI-element for Stokes equations %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2014 %P 955-968 %V 48 %N 4 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013129/ %R 10.1051/m2an/2013129 %G en %F M2AN_2014__48_4_955_0
Kwon, Oh-In; Park, Chunjae. A new quadrilateral MINI-element for Stokes equations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 4, pp. 955-968. doi: 10.1051/m2an/2013129
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