no. 4
A new quadrilateral MINI-element for Stokes equations
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 4, pp. 955-968

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.

DOI : 10.1051/m2an/2013129
Classification : 65N30, 74S05, 76M10
Keywords: MINI-element, superconvergence 
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     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},
     year = {2014},
     publisher = {EDP Sciences},
     volume = {48},
     number = {4},
     doi = {10.1051/m2an/2013129},
     mrnumber = {3264342},
     zbl = {1299.76140},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/m2an/2013129/}
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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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