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
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