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A new quadrilateral MINI-element for Stokes equations

Oh-In Kwon;  Chunjae Park — 2014

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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 -midpoint-edge-continuous elements and each component of the velocity field is done with the standard Q-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...

A piecewise P2-nonconforming quadrilateral finite element

Imbunm Kim;  Zhongxuan Luo;  Zhaoliang Meng;  Hyun NAM;  Chunjae Park;  Dongwoo Sheen — 2013

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We introduce a piecewise -nonconforming quadrilateral finite element. First, we decompose a convex quadrilateral into the union of four triangles divided by its diagonals. Then the finite element space is defined by the set of all piecewise -polynomials that are quadratic in each triangle and continuously differentiable on the quadrilateral. The degrees of freedom (DOFs) are defined by the eight values at the two Gauss points on each of the four edges plus the value...

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