no. 6
A class of nonparametric DSSY nonconforming quadrilateral elements
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 47 (2013) no. 6, pp. 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 : 10.1051/m2an/2013088
Classification : 65N30
Mots clés : nonconforming, finite element, quadrilateral 
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     title = {A class of nonparametric {DSSY} nonconforming quadrilateral elements},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1783--1796},
     publisher = {EDP-Sciences},
     volume = {47},
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     year = {2013},
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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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