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A class of nonparametric DSSY nonconforming quadrilateral elements

Youngmok JeonHyun NAMDongwoo SheenKwangshin Shim — 2013

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

A new class of nonparametric nonconforming quadrilateral finite elements is introduced which has the midpoint continuity and the mean value continuity at the interfaces of elements simultaneously as the rectangular DSSY element [J. Douglas, Jr., J.E. Santos, D. Sheen and X. Ye, 33 (1999) 747–770.] The parametric DSSY element for general quadrilaterals requires five degrees of freedom to have an optimal order of convergence [Z. Cai, J. Douglas, Jr., J.E. Santos, D. Sheen and X. Ye, 37 (2000) 253–254.],...

A piecewise P2-nonconforming quadrilateral finite element

Imbunm KimZhongxuan LuoZhaoliang MengHyun NAMChunjae ParkDongwoo 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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