| Issue |
ESAIM: M2AN
Volume 41, Number 5, September-October 2007
|
|
|---|---|---|
| Page(s) | 855 - 874 | |
| DOI | https://doi.org/10.1051/m2an:2007034 | |
| Published online | 23 October 2007 | |
Inf-sup stable nonconforming finite elements of higher order on quadrilaterals and hexahedra
Fakultät für Mathematik, Ruhr-Universität Bochum,
Universitätsstraße 150, 44780 Bochum, Germany. Gunar.Matthies@ruhr-uni-bochum.de
Received:
25
October
2005
We present families of scalar nonconforming finite elements of arbitrary
order 
with optimal approximation properties on quadrilaterals and
hexahedra. Their vector-valued versions together with a discontinuous
pressure approximation of order 
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.
Mathematics Subject Classification: 65N12 / 65N30
Key words: Nonconforming finite elements / inf-sup stability / quadrilaterals / hexahedra.
© EDP Sciences, SMAI, 2007
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