Some nonconforming finite elements for the plate bending problem

P. Lascaux; P. Lesaint

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1975)

  • Volume: 9, Issue: R1, page 9-53
  • ISSN: 0764-583X

How to cite

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Lascaux, P., and Lesaint, P.. "Some nonconforming finite elements for the plate bending problem." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 9.R1 (1975): 9-53. <http://eudml.org/doc/193267>.

@article{Lascaux1975,
author = {Lascaux, P., Lesaint, P.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
language = {eng},
number = {R1},
pages = {9-53},
publisher = {Dunod},
title = {Some nonconforming finite elements for the plate bending problem},
url = {http://eudml.org/doc/193267},
volume = {9},
year = {1975},
}

TY - JOUR
AU - Lascaux, P.
AU - Lesaint, P.
TI - Some nonconforming finite elements for the plate bending problem
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1975
PB - Dunod
VL - 9
IS - R1
SP - 9
EP - 53
LA - eng
UR - http://eudml.org/doc/193267
ER -

References

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  1. [l] 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 Galerkiris and finite difference methods. Ann. Scuola Norm. Sup. Pisa 21, 599-637, 1967. Zbl0276.65052MR233068
  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.F.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.Expérience 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 COn the convergence of a mixed finite element method for plate bending problems Numer Math 21, 43-62, 1973 Zbl0264.65070MR388807
  12. [12] KONDRATEV VABoundary value problems for elliptic equations with conical or angular points Trans Moscow Math Soc ,227-313, 1967 Zbl0194.13405
  13. [13] LANDAU L - LIFCHITZ ETheory of Elasticity Pergamon Press 1970 
  14. [14] LIONS JL - MAGENES EProblèmes aux limites non-homogènes Dunod, 1968 
  15. [15] MORLEY L S DThe triangular equilibrium element in the solution of plate bending problems Aero-Quart 19, 149-169, 1968 
  16. [16] MlYOSHY TConvergence of finite element solutions represented by a non-conforming basis Kumamoto J Sci Math 9, 11-20, 1972 Zbl0236.65071MR309411
  17. [17] NITSCHE JConvergence of non conforming elements Symposium on Mathematical Aspects of Finite Elements in Partial Differential Equations, Madison, Wisconsin, April 1-3, 1974 Zbl0324.00023
  18. [18] NlTSCHE JEin Kriterium für die Quasi-optimalitat des Ritzschen Verfahrens Numer Math. 13, 260-265, 1969. Zbl0175.45801
  19. [19] STRANG GVariational Crimes in the finite element method The mathematical 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 GAn analysis of the Finite Element Method Prentice Hall, Englewood Cliffs, 1973 Zbl0356.65096MR443377
  21. [21] ZIENKIEWICZ OCThe Finite Element Method in Engineering Science Mac Graw-Hill, London, 1971 Zbl0237.73071MR315970

Citations in EuDML Documents

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  1. M. I. Comodi, Approximation of a fourth order variational inequality
  2. Rolf Rannacher, On nonconforming an mixed finite element methods for plate bending problems. The linear case
  3. Friedrich Stummel, Basic compactness properties of nonconforming and hybrid finite element spaces
  4. Pavel Bělík, Timothy Brule, Mitchell Luskin, On the numerical modeling of deformations of pressurized martensitic thin films
  5. Jim Jr. Douglas, Juan E. Santos, Dongwoo Sheen, Xiu Ye, Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems
  6. Pavel Bělík, Timothy Brule, Mitchell Luskin, On the Numerical Modeling of Deformations of Pressurized Martensitic Thin Films
  7. Hiroki Ishizaka, Morley finite element analysis for fourth-order elliptic equations under a semi-regular mesh condition
  8. D. N. Arnold, F. Brezzi, Mixed and nonconforming finite element methods : implementation, postprocessing and error estimates
  9. Andrey Andreev, Milena Racheva, Two-sided bounds of eigenvalues of second- and fourth-order elliptic operators

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