A new quadrilateral MINI-element for Stokes equations
Kwon, Oh-In ; Park, Chunjae
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 48 (2014), p. 955-968 / Harvested from Numdam
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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.

Publié le : 2014-01-01
DOI : https://doi.org/10.1051/m2an/2013129
Classification:  65N30,  74S05,  76M10 
@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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {48},
     year = {2014},
     pages = {955-968},
     doi = {10.1051/m2an/2013129},
     mrnumber = {3264342},
     zbl = {1299.76140},
     language = {en},
     url = {http://dml.mathdoc.fr/item/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 - Modélisation Mathématique et Analyse Numérique, Tome 48 (2014) pp. 955-968. doi : 10.1051/m2an/2013129. http://gdmltest.u-ga.fr/item/M2AN_2014__48_4_955_0/

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