Éléments finis non-conformes pour le problème de la flexion des plaques minces

P. Lascaux; P. Lesaint

Publications mathématiques et informatique de Rennes (1974)

  • Issue: S4, page 1-58

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Lascaux, P., and Lesaint, P.. "Éléments finis non-conformes pour le problème de la flexion des plaques minces." Publications mathématiques et informatique de Rennes (1974): 1-58. <http://eudml.org/doc/274663>.

@article{Lascaux1974,
author = {Lascaux, P., Lesaint, P.},
journal = {Publications mathématiques et informatique de Rennes},
language = {fre},
number = {S4},
pages = {1-58},
publisher = {Département de Mathématiques et Informatique, Université de Rennes},
title = {Éléments finis non-conformes pour le problème de la flexion des plaques minces},
url = {http://eudml.org/doc/274663},
year = {1974},
}

TY - JOUR
AU - Lascaux, P.
AU - Lesaint, P.
TI - Éléments finis non-conformes pour le problème de la flexion des plaques minces
JO - Publications mathématiques et informatique de Rennes
PY - 1974
PB - Département de Mathématiques et Informatique, Université de Rennes
IS - S4
SP - 1
EP - 58
LA - fre
UR - http://eudml.org/doc/274663
ER -

References

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  1. /1/ Adini A. ; Clough R.W. - Analysis of plate bending by the finite element method - NSF Report G.7337, 1961. 
  2. /2/ Aubin J.P. - Behavior of the error of the approximate solutions of boundary value problems for linear elliptic operators by Galerkin's and finite difference methods. Ann. Scuole Norr, Sup. Pisa21 , 599-637, 1967 Zbl0276.65052
  3. /3/ Bazeley G.P. ; Cheung Y.K. ; Irons B.M. ; Zienkiewicz O.C.Triangular elements in bending-conforming and nonconforming solutions. Proceedings Conference on Matrix Methods in Structural Mechanics, Wright Patterson A.K.B., Ohio, 1965 
  4. /4/ Ciarlet P.G. - Conforming and Nonconforming finite element methods for solving the plate problem. Proceedings Conference on the Numerical Solution of Differential Equations, University of Dundee, July 03-06, 1973. Zbl0285.65072MR423832
  5. /5/ Ciarlet P.G, - Quelques méthodes d'éléments finis pour le problème d'une plaque encastrée. Colloques IRIA, Méthodes de Calcul Scientifique et Technique, 66-86, Rocquencourt, 1973. Zbl0285.65042
  6. /6/ Ciarlet P.G. ; Raviart P.A. - General Lagrange and Hermite interpolation In R n with applications to finite element methods. Arch. Rational Mech. Anal.46, 177-199, 1972. Zbl0243.41004MR336957
  7. /7/ Ciarlet P.G. ; Raviart P.A. - Error bounds for finite elements "with normal derivatives" (to appear). 
  8. /8/ Crouzeix M. ; Raviart P.A. - Conforming and nonconforming finite element methods for solving the stationary Stokes equations. I (to appear). Zbl0302.65087MR343661
  9. /9/ Fraeijs de Veubeke B. - Variational .Principles and the Patch Test (to appear). Zbl0284.73043
  10. /10/ Irons B.M. ; Razzaque A. - Experience with the patch test for convergence of finite elements. The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (A.K. Aziz, Editor), 557-587 - Academic Press, New York, 1972. Zbl0279.65087MR423839
  11. /11/ Johnson C. - On the convergence of a mixed finite element method for plate bending problems. Numer Math21, 43-62, 1973. Zbl0264.65070MR388807
  12. /12/ Kondratev V.A. - Boundary value problems for elliptic equations with conical or angular points. Trans. Moscow Math. Soc., 227-313, 1967. Zbl0194.13405
  13. /13/ Landau L. ; Lifchitz E. - Theory of Elasticity - Pergamon Press1970. 
  14. /14/ Lions J.L. ; Magenes E. - Problèmes aux limites non-homogènes - Dunod, 1968. Zbl0117.06904
  15. /15/ Morley L.S.D. - The triangular equilibrium element in the solution of plate bending problems, Aero-Quart.19, 149-169, 1968. 
  16. /16/ Minoshi T. - Convergence of finite clement solutions represented by a non-conforming basis, Kumamoto J. Sci. Math.9, 11-20, 1972. Zbl0236.65071MR309411
  17. /17/ Nitsche J. - Convergence of non conforming elements. Symposium on Mathematical Aspects of Finite Elements in Partial Differential Equations, Madison, Wisconsin, April 1-3, 1974. 
  18. /18/ Nitsche J. - Ein Kriterium fur die Quasi-optimalitat des Ritzschen Verfahrens. Numer. Math.13, 260-265, 1969. Zbl0181.18204MR233502
  19. /19/ Strang G. - Variational Crimes in the finite element method. The Matematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (A.K. Aziz, Editor), 689-710, Academic Press, New York, 1972. Zbl0264.65068MR413554
  20. /20/ Strang G. ; Fix G. - An analysis of the Finite Element Method, Prentice Hall, Englewood Cliffs, 1973. Zbl0356.65096MR443377
  21. /21/ Zienkiewicz O.C. - The finite Element Method in Engineering Science, Mac Graw-Hill, London, 1971. Zbl0237.73071MR315970
  22. /22/ Lascaux P. et Lesaint P. - Some non conforming finite elements for the plate bending problem. To appear in R.A.I.R.O. Zbl0319.73042MR423968

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