Geodesic
Inf-sup stable nonconforming finite elements of higher order on quadrilaterals and hexahedra
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 41 (2007) no. 5, pp. 855-874

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We present families of scalar nonconforming finite elements of arbitrary order r≥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.

DOI : 10.1051/m2an:2007034
Classification : 65N12, 65N30
Keywords: nonconforming finite elements, inf-sup stability, quadrilaterals, hexahedra 
Matthies, Gunar. Inf-sup stable nonconforming finite elements of higher order on quadrilaterals and hexahedra. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 41 (2007) no. 5, pp. 855-874. doi: 10.1051/m2an:2007034
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     title = {Inf-sup stable nonconforming finite elements of higher order on quadrilaterals and hexahedra},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {855--874},
     year = {2007},
     publisher = {EDP-Sciences},
     volume = {41},
     number = {5},
     doi = {10.1051/m2an:2007034},
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     zbl = {1147.65094},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2007034/}
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