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Inf-sup stable nonconforming finite elements of higher order onquadrilaterals and hexahedra

Published online by Cambridge University Press:  23 October 2007

Gunar Matthies
Gunar Matthies*
Affiliation:
Fakultät für Mathematik, Ruhr-Universität Bochum, Universitätsstraße 150, 44780 Bochum, Germany. Gunar.Matthies@ruhr-uni-bochum.de
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Abstract

We present families of scalar nonconforming finite elements of arbitrary order $r\ge 1$ with optimal approximation properties on quadrilaterals and hexahedra. Their vector-valued versions together with a discontinuous pressure approximation of order $r-1$ form inf-sup stable finite element pairs of order r for the Stokes problem. The well-known elements by Rannacher and Turek are recovered in the case r=1. A numerical comparison between conforming and nonconforming discretisations will be given. Since higher order nonconforming discretisation on quadrilaterals and hexahedra have less unknowns and much less non-zero matrix entries compared to corresponding conforming methods, these methods are attractive for numerical simulations.

Keywords

Nonconforming finite elementsinf-sup stabilityquadrilateralshexahedra.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 41 , Issue 5 , September 2007 , pp. 855 - 874
Copyright
© EDP Sciences, SMAI, 2007

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