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mini-element

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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A new quadrilateral MINI-element for Stokes equations
Oh-In Kwon, Chunjae Park
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 48 / Issue 4 / July 2014

Published online by Cambridge University Press:

30 June 2014, pp. 955-968

Print publication:

July 2014
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We introduce a new stable MINI-element pair for incompressible Stokes equations onquadrilateral meshes, which uses the smallest number of bubbles for the velocity. Thepressure is discretized with the P1-midpoint-edge-continuous elements and each component of the velocity field is done withthe standard Q1-conforming elements enriched byone bubble a quadrilateral. The superconvergence in the pressure of the proposed pair isanalyzed on uniform rectangular meshes, and tested numerically on uniform and non-uniformmeshes.