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

Gunar Matthies

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

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

Abstract

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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.

How to cite

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Matthies, 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 -

References

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