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Some nonconforming finite elements for the plate bending problem. (English) Zbl 0319.73042

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74K20 Plates
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References:
[1] 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. Zbl0276.65052 MR233068 · Zbl 0276.65052 · numdam:ASNSP_1967_3_21_4_599_0 · eudml:83439
[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. Zbl0285.65072 MR423832 · Zbl 0285.65072
[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 · Zbl 0285.65042
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[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). Zbl0302.65087 MR343661 · Zbl 0302.65087 · eudml:193250
[9] FRAEIJS DE VEUBEKE B.Variational Principles and the Patch Test. (to appear). Zbl0284.73043 · Zbl 0284.73043 · doi:10.1002/nme.1620080408
[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. Zbl0279.65087 MR423839 · Zbl 0279.65087
[11] JOHNSON COn the convergence of a mixed finite element method for plate bending problems Numer Math 21, 43-62, 1973 Zbl0264.65070 MR388807 · Zbl 0264.65070 · doi:10.1007/BF01436186 · eudml:132212
[12] KONDRATEV VABoundary value problems for elliptic equations with conical or angular points Trans Moscow Math Soc ,227-313, 1967 Zbl0194.13405 · Zbl 0194.13405
[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 Zbl0236.65071 MR309411 · Zbl 0236.65071
[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 · Zbl 0324.00023
[18] NlTSCHE JEin Kriterium für die Quasi-optimalitat des Ritzschen Verfahrens Numer Math. 13, 260-265, 1969. Zbl0175.45801 · Zbl 0175.45801 · doi:10.1007/BF02166687 · eudml:131833
[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 Zbl0264.65068 MR413554 · Zbl 0264.65068
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[21] ZIENKIEWICZ OCThe Finite Element Method in Engineering Science Mac Graw-Hill, London, 1971 Zbl0237.73071 MR315970 · Zbl 0237.73071
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