A class of nonparametric DSSY nonconforming quadrilateral elements
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 47 (2013) no. 6, p. 1783-1796

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.

DOI : https://doi.org/10.1051/m2an/2013088
Classification:  65N30
Keywords: 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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {47},
     number = {6},
     year = {2013},
     pages = {1783-1796},
     doi = {10.1051/m2an/2013088},
     zbl = {1287.65109},
     mrnumber = {3123376},
     language = {en},
     url = {http://www.numdam.org/item/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 - Modélisation Mathématique et Analyse Numérique, Volume 47 (2013) no. 6, pp. 1783-1796. doi : 10.1051/m2an/2013088. http://www.numdam.org/item/M2AN_2013__47_6_1783_0/

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