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A class of nonparametric DSSY nonconforming quadrilateralelements∗

Published online by Cambridge University Press:  07 October 2013

Youngmok Jeon ,
Hyun Nam ,
Dongwoo Sheen  and
Kwangshin Shim
Youngmok Jeon
Affiliation:
Department of Mathematics, Ajou University, Suwon 443–749, Korea.. yjeon@ajou.ac.kr
Hyun Nam
Affiliation:
Department of Mathematics, Seoul National University, Seoul 151–747, Korea.; lamyun96@snu.ac.kr
Dongwoo Sheen
Affiliation:
Department of Mathematics, and Interdisciplinary Program in Computational Science and Technology, Seoul National University, Seoul 151–747, Korea.; sheen@snu.ac.kr
Kwangshin Shim
Affiliation:
Department of Mathematics, Seoul National University, Seoul 151–747, Korea.; sim4322@snu.ac.kr
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Abstract

A new class of nonparametric nonconforming quadrilateral finite elements is introducedwhich has the midpoint continuity and the mean value continuity at the interfaces ofelements simultaneously as the rectangular DSSY element [J. Douglas, Jr., J.E. Santos, D.Sheen and X. Ye, ESAIM: M2AN 33 (1999) 747–770.] Theparametric DSSY element for general quadrilaterals requires five degrees of freedom tohave an optimal order of convergence [Z. Cai, J. Douglas, Jr., J.E. Santos, D. Sheen andX. Ye, Calcolo 37 (2000) 253–254.], while the newnonparametric DSSY elements require only four degrees of freedom. The design of newelements is based on the decomposition of a bilinear transform into a simple bilinear mapfollowed by a suitable affine map. Numerical results are presented to compare the newelements with the parametric DSSY element.

Keywords

Nonconformingfinite elementquadrilateral
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 6 , November 2013 , pp. 1783 - 1796
Copyright
© EDP Sciences, SMAI 2013

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