Éléments finis non-conformes pour le problème de la flexion des plaques minces
Publications mathématiques et informatique de Rennes, no. S4 (1974), article no. 6, 58 p.
@article{PSMIR_1974___S4_A6_0,
     author = {Lascaux, P. and Lesaint, Pierre},
     title = {\'El\'ements finis non-conformes pour le probl\`eme de la flexion des plaques minces},
     journal = {Publications math\'ematiques et informatique de Rennes},
     eid = {6},
     publisher = {D\'epartement de Math\'ematiques et Informatique, Universit\'e de Rennes},
     number = {S4},
     year = {1974},
     language = {fr},
     url = {http://archive.numdam.org/item/PSMIR_1974___S4_A6_0/}
}
Lascaux, P.; Lesaint, P. Éléments finis non-conformes pour le problème de la flexion des plaques minces. Publications mathématiques et informatique de Rennes, no. S4 (1974), article  no. 6, 58 p. http://archive.numdam.org/item/PSMIR_1974___S4_A6_0/

/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 Galerkin's and finite difference methods. Ann. Scuole Norr, Sup. Pisa 21 , 599-637, 1967 | Numdam | Zbl 0276.65052

/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/ 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. | MR 423832 | 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. | Zbl 0285.65042

/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. | MR 336957 | Zbl 0243.41004

/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). | Numdam | MR 343661 | Zbl 0302.65087

/9/ Fraeijs De Veubeke B. - Variational .Principles and the Patch Test (to appear). | Zbl 0284.73043

/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. | MR 423839 | Zbl 0279.65087

/11/ Johnson C. - On the convergence of a mixed finite element method for plate bending problems. Numer Math 21, 43-62, 1973. | MR 388807 | Zbl 0264.65070

/12/ Kondratev V.A. - Boundary value problems for elliptic equations with conical or angular points. Trans. Moscow Math. Soc., 227-313, 1967. | Zbl 0194.13405

/13/ Landau L. ; Lifchitz E. - Theory of Elasticity - Pergamon Press 1970.

/14/ Lions J.L. ; Magenes E. - Problèmes aux limites non-homogènes - Dunod, 1968. | Zbl 0117.06904

/15/ Morley L.S.D. - The triangular equilibrium element in the solution of plate bending problems, Aero-Quart. 19, 149-169, 1968.

/16/ Minoshi T. - Convergence of finite clement solutions represented by a non-conforming basis, Kumamoto J. Sci. Math. 9, 11-20, 1972. | MR 309411 | Zbl 0236.65071

/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/ Nitsche J. - Ein Kriterium fur die Quasi-optimalitat des Ritzschen Verfahrens. Numer. Math. 13, 260-265, 1969. | MR 233502 | Zbl 0181.18204

/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. | MR 413554 | Zbl 0264.65068

/20/ Strang G. ; Fix G. - An analysis of the Finite Element Method, Prentice Hall, Englewood Cliffs, 1973. | MR 443377 | Zbl 0356.65096

/21/ Zienkiewicz O.C. - The finite Element Method in Engineering Science, Mac Graw-Hill, London, 1971. | MR 315970 | Zbl 0237.73071

/22/ Lascaux P. et Lesaint P. - Some non conforming finite elements for the plate bending problem. To appear in R.A.I.R.O. | Numdam | MR 423968 | Zbl 0319.73042