Conforming and nonconforming finite element methods for solving the stationary Stokes equations I

M. Crouzeix; P.-A. Raviart

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1973)

  • Volume: 7, Issue: R3, page 33-75
  • ISSN: 0764-583X

How to cite

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Crouzeix, M., and Raviart, P.-A.. "Conforming and nonconforming finite element methods for solving the stationary Stokes equations I." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 7.R3 (1973): 33-75. <http://eudml.org/doc/193250>.

@article{Crouzeix1973,
author = {Crouzeix, M., Raviart, P.-A.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
language = {eng},
number = {R3},
pages = {33-75},
publisher = {Dunod},
title = {Conforming and nonconforming finite element methods for solving the stationary Stokes equations I},
url = {http://eudml.org/doc/193250},
volume = {7},
year = {1973},
}

TY - JOUR
AU - Crouzeix, M.
AU - Raviart, P.-A.
TI - Conforming and nonconforming finite element methods for solving the stationary Stokes equations I
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1973
PB - Dunod
VL - 7
IS - R3
SP - 33
EP - 75
LA - eng
UR - http://eudml.org/doc/193250
ER -

References

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  1. [1] BAZELEY G. P., CHEUNG Y. K., IRONS B. M. et ZIENKIEWICZ O. C., Triangular elements in bending-conforming and nonconforming solutions, Proc. Conf. Matrix Methods in Structural Mechanics, Air Forces Inst. of Tech., Wright Patterson A. F. Base, Ohio, 1965. 
  2. [2] BOLLEY P. et CAMUS J., (to appear). 
  3. [3] BRAMBLE J. H. et HILBERT S. R., Estimations of linear functionals on Sobolev spaces with applications to Fourier transforms and spline interpolation, J. Numer. Anal., 7, 1970, 112-124. Zbl0201.07803MR263214
  4. [4] CATTABRIGA L., Su un problema al contorno relativo al sistema di equazioni di Stokes. Rend. Sem. Mat. Padova, 1961, 1-33. Zbl0116.18002
  5. [5] CIARLET P. G. et RAVIART P.-A., General Lagrange and Hermite interpolation in R n with applications to finite element methods, Arch. Rat. Mech. Anal., 46, 1972, 177-199. Zbl0243.41004MR336957
  6. [6] CIARLET P. G. et RAVIART P.-A., Interpolation theory over curved elements with applications to finite element methods, Computer Meth. Appl. Mech. Engin., 1, 1972, 217-249. Zbl0261.65079MR375801
  7. [7] CIARLET P. G. et RAVIART P.-A., The combined effect of curved boundaries and numerical integration in isoparametric finite element methods. The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (A. K. Aziz, ed.), 409-474, Academic Press, New-York, 1972. Zbl0262.65070MR421108
  8. [8] FORTIN M., Calcul numérique des écoulements des fluides de Bingham et des fluides newtoniens incompressibles par la méthode des éléments finis, Thèse, Université de Paris VI, 1972. 
  9. [9] FORTIN M., Résolution des équations des fluides incompressibles par la méthode des éléments finis (to appear in Proc. 3rd Int. Conf. on the Numerical Methods in Fluid Mechanics, Paris, July 3-7, 1972, Springer Verlag). 
  10. [10] IRONS B. M et RAZZAQUE A., Experience with the pach test for convergence of finite elements, The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (A. K. Aziz, ed.), 557-588, Academic Press, New-York, 1972. Zbl0279.65087MR423839
  11. [11] JAMET P. et RAVIART P.-A., Numerical Solution of the Stationary Navier-Stokes equations by finite element methods (to appear). Zbl0285.76007
  12. [12] LADYZHENSKAYA O. A., The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach, New-York, 1962. Zbl0121.42701
  13. [13] LIONS J.-L., Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris, 1969. Zbl0189.40603MR259693
  14. [14] DE RHAM, Variétés différentiables, Hermann, Paris, 1960. Zbl0089.08105
  15. [15] STRANG G. et FIX G., An Analysis of the Finite Element Method, Prentice Hall, New-York, 1973. Zbl0356.65096
  16. [16] ZIENKIEWICZ O. C., The Finite Element Method in Engineering Science, Mc Graw Hill, London, 1971. Zbl0237.73071

Citations in EuDML Documents

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  1. Peter Hansbo, Mats G. Larson, Discontinuous Galerkin and the Crouzeix–Raviart element : application to elasticity
  2. M. Crouzeix, A. Y. Le Roux, Écoulement d'un fluide irrotationnel
  3. R. Glowinski, O. Pironneau, On Numerical Methods for the Stokes Problem
  4. F. Hecht, Construction d’une base de fonctions P 1 non conforme à divergence nulle dans 3
  5. Peter Hansbo, Mats G. Larson, Discontinuous Galerkin and the Crouzeix–Raviart element: Application to elasticity
  6. Youngmok Jeon, Hyun NAM, Dongwoo Sheen, Kwangshin Shim, A class of nonparametric DSSY nonconforming quadrilateral elements
  7. Thirupathi Gudi, Johnny Guzmán, Convergence analysis of the lowest order weakly penalized adaptive discontinuous Galerkin methods
  8. B. Mercier, Régularisation, approximation et résolution du problème des charges limites
  9. B. Courbet, J. P. Croisille, Finite volume box schemes on triangular meshes
  10. F. Schieweck, L. Tobiska, A nonconforming finite element method of upstream type applied to the stationary Navier-Stokes equation

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