# Inf-sup stable nonconforming finite elements of higher order on quadrilaterals and hexahedra

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

- Volume: 41, Issue: 5, page 855-874
- ISSN: 0764-583X

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topMatthies, Gunar. "Inf-sup stable nonconforming finite elements of higher order on quadrilaterals and hexahedra." ESAIM: Mathematical Modelling and Numerical Analysis 41.5 (2007): 855-874. <http://eudml.org/doc/250052>.

@article{Matthies2007,

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.
},

author = {Matthies, Gunar},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Nonconforming finite elements; inf-sup stability;
quadrilaterals; hexahedra.; Stokes problem; finite element method; posteriori error; numerical examples},

language = {eng},

month = {10},

number = {5},

pages = {855-874},

publisher = {EDP Sciences},

title = {Inf-sup stable nonconforming finite elements of higher order on quadrilaterals and hexahedra},

url = {http://eudml.org/doc/250052},

volume = {41},

year = {2007},

}

TY - JOUR

AU - Matthies, Gunar

TI - Inf-sup stable nonconforming finite elements of higher order on quadrilaterals and hexahedra

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2007/10//

PB - EDP Sciences

VL - 41

IS - 5

SP - 855

EP - 874

AB -
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.

LA - eng

KW - Nonconforming finite elements; inf-sup stability;
quadrilaterals; hexahedra.; Stokes problem; finite element method; posteriori error; numerical examples

UR - http://eudml.org/doc/250052

ER -

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