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 for the Stokes problem. The well-known elements by Rannacher and Turek are recovered in the case . 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 elements, inf-sup stability, quadrilaterals, hexahedra
@article{M2AN_2007__41_5_855_0,
author = {Matthies, Gunar},
title = {Inf-sup stable nonconforming finite elements of higher order on quadrilaterals and hexahedra},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {855--874},
year = {2007},
publisher = {EDP Sciences},
volume = {41},
number = {5},
doi = {10.1051/m2an:2007034},
mrnumber = {2363886},
zbl = {1147.65094},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an:2007034/}
}
TY - JOUR AU - Matthies, Gunar TI - Inf-sup stable nonconforming finite elements of higher order on quadrilaterals and hexahedra JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2007 SP - 855 EP - 874 VL - 41 IS - 5 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an:2007034/ DO - 10.1051/m2an:2007034 LA - en ID - M2AN_2007__41_5_855_0 ER -
%0 Journal Article %A Matthies, Gunar %T Inf-sup stable nonconforming finite elements of higher order on quadrilaterals and hexahedra %J ESAIM: Modélisation mathématique et analyse numérique %D 2007 %P 855-874 %V 41 %N 5 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an:2007034/ %R 10.1051/m2an:2007034 %G en %F M2AN_2007__41_5_855_0
Matthies, Gunar. Inf-sup stable nonconforming finite elements of higher order on quadrilaterals and hexahedra. ESAIM: Modélisation mathématique et analyse numérique, Tome 41 (2007) no. 5, pp. 855-874. doi: 10.1051/m2an:2007034
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