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, ESAIM: M2AN 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, Calcolo 37 (2000) 253-254.], while the new nonparametric DSSY elements require only four degrees of freedom. The design of new elements is based on the decomposition of a bilinear transform into a simple bilinear map followed by a suitable affine map. Numerical results are presented to compare the new elements with the parametric DSSY element.
Mots-clés : nonconforming, finite element, quadrilateral
@article{M2AN_2013__47_6_1783_0,
author = {Jeon, Youngmok and NAM, Hyun and Sheen, Dongwoo and Shim, Kwangshin},
title = {A class of nonparametric {DSSY} nonconforming quadrilateral elements},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1783--1796},
publisher = {EDP-Sciences},
volume = {47},
number = {6},
year = {2013},
doi = {10.1051/m2an/2013088},
mrnumber = {3123376},
zbl = {1287.65109},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2013088/}
}
TY - JOUR AU - Jeon, Youngmok AU - NAM, Hyun AU - Sheen, Dongwoo AU - Shim, Kwangshin TI - A class of nonparametric DSSY nonconforming quadrilateral elements JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2013 SP - 1783 EP - 1796 VL - 47 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2013088/ DO - 10.1051/m2an/2013088 LA - en ID - M2AN_2013__47_6_1783_0 ER -
%0 Journal Article %A Jeon, Youngmok %A NAM, Hyun %A Sheen, Dongwoo %A Shim, Kwangshin %T A class of nonparametric DSSY nonconforming quadrilateral elements %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2013 %P 1783-1796 %V 47 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2013088/ %R 10.1051/m2an/2013088 %G en %F M2AN_2013__47_6_1783_0
Jeon, Youngmok; NAM, Hyun; Sheen, Dongwoo; Shim, Kwangshin. A class of nonparametric DSSY nonconforming quadrilateral elements. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 47 (2013) no. 6, pp. 1783-1796. doi : 10.1051/m2an/2013088. http://www.numdam.org/articles/10.1051/m2an/2013088/
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