Some nonconforming finite elements for the plate bending problem
- Volume: 9, Issue: R1, page 9-53
- ISSN: 0764-583X
Access Full Article
topHow to cite
topLascaux, 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
top- [l] ADINI A . - CLOUGH R.W.Analysis of plate bending by the finite element method. NSF Report G. 7337, 1961.
- [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] 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] 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] 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] CIARLET P.G. - RAVIART P.A.General Lagrange and Hermite interpolation in with applications to finite element methods. Arch. Rational Mech. Anal. 46, 177-199, 1972. Zbl0243.41004MR336957
- [7] CIARLET P.G - RAVIART P.A.Error bounds for finite elements "with normal derivatives" (to appear).
- [8] CROUZEIX M. - RAVIART P.A.Conforming and nonconforming finite element methods for solving the stationary Stokes equations. I (to appear). Zbl0302.65087MR343661
- [9] FRAEIJS DE VEUBEKE B.Variational Principles and the Patch Test. (to appear). Zbl0284.73043
- [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] JOHNSON COn the convergence of a mixed finite element method for plate bending problems Numer Math 21, 43-62, 1973 Zbl0264.65070MR388807
- [12] KONDRATEV VABoundary value problems for elliptic equations with conical or angular points Trans Moscow Math Soc ,227-313, 1967 Zbl0194.13405
- [13] LANDAU L - LIFCHITZ ETheory of Elasticity Pergamon Press 1970
- [14] LIONS JL - MAGENES EProblèmes aux limites non-homogènes Dunod, 1968
- [15] MORLEY L S DThe triangular equilibrium element in the solution of plate bending problems Aero-Quart 19, 149-169, 1968
- [16] MlYOSHY TConvergence of finite element solutions represented by a non-conforming basis Kumamoto J Sci Math 9, 11-20, 1972 Zbl0236.65071MR309411
- [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] NlTSCHE JEin Kriterium für die Quasi-optimalitat des Ritzschen Verfahrens Numer Math. 13, 260-265, 1969. Zbl0175.45801
- [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] STRANG G - FIX GAn analysis of the Finite Element Method Prentice Hall, Englewood Cliffs, 1973 Zbl0356.65096MR443377
- [21] ZIENKIEWICZ OCThe Finite Element Method in Engineering Science Mac Graw-Hill, London, 1971 Zbl0237.73071MR315970
Citations in EuDML Documents
top- M. I. Comodi, Approximation of a fourth order variational inequality
- Rolf Rannacher, On nonconforming an mixed finite element methods for plate bending problems. The linear case
- Friedrich Stummel, Basic compactness properties of nonconforming and hybrid finite element spaces
- Pavel Bělík, Timothy Brule, Mitchell Luskin, On the numerical modeling of deformations of pressurized martensitic thin films
- Jim Jr. Douglas, Juan E. Santos, Dongwoo Sheen, Xiu Ye, Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems
- Pavel Bělík, Timothy Brule, Mitchell Luskin, On the Numerical Modeling of Deformations of Pressurized Martensitic Thin Films
- D. N. Arnold, F. Brezzi, Mixed and nonconforming finite element methods : implementation, postprocessing and error estimates
- Andrey Andreev, Milena Racheva, Two-sided bounds of eigenvalues of second- and fourth-order elliptic operators
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.