On the numerical solution of plate bending problems by hybrid methods
Revue française d'automatique, informatique, recherche opérationnelle. Analyse numérique, Tome 9 (1975) no. R3, pp. 5-50.
@article{M2AN_1975__9_3_5_0,
     author = {Brezzi, F. and Marini, L. D.},
     title = {On the numerical solution of plate bending problems by hybrid methods},
     journal = {Revue fran\c{c}aise d'automatique, informatique, recherche op\'erationnelle. Analyse num\'erique},
     pages = {5--50},
     publisher = {Dunod},
     address = {Paris},
     volume = {9},
     number = {R3},
     year = {1975},
     zbl = {0322.73048},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1975__9_3_5_0/}
}
TY  - JOUR
AU  - Brezzi, F.
AU  - Marini, L. D.
TI  - On the numerical solution of plate bending problems by hybrid methods
JO  - Revue française d'automatique, informatique, recherche opérationnelle. Analyse numérique
PY  - 1975
SP  - 5
EP  - 50
VL  - 9
IS  - R3
PB  - Dunod
PP  - Paris
UR  - http://www.numdam.org/item/M2AN_1975__9_3_5_0/
LA  - en
ID  - M2AN_1975__9_3_5_0
ER  - 
%0 Journal Article
%A Brezzi, F.
%A Marini, L. D.
%T On the numerical solution of plate bending problems by hybrid methods
%J Revue française d'automatique, informatique, recherche opérationnelle. Analyse numérique
%D 1975
%P 5-50
%V 9
%N R3
%I Dunod
%C Paris
%U http://www.numdam.org/item/M2AN_1975__9_3_5_0/
%G en
%F M2AN_1975__9_3_5_0
Brezzi, F.; Marini, L. D. On the numerical solution of plate bending problems by hybrid methods. Revue française d'automatique, informatique, recherche opérationnelle. Analyse numérique, Tome 9 (1975) no. R3, pp. 5-50. http://www.numdam.org/item/M2AN_1975__9_3_5_0/

[1] A. Adini and R. W. Clough, Analysis of plate bending by the finite element method, NSF Report G. 7337, 1961.

[2] F. K. Bogner, R. L. Fox and L. A. Schmit, The generation of interelement compatible stiffness and mass matrices by the use of interpolation formulas, Conference on Matric Methods in Structural Mechanics, Wright Patterson A.F.B., Ohio, 1965.

[3] J. H. Bramble and R. S. Hilbert, Estimation of linear functionals on Sobolev Spaces with applications to Fourier transforms andspline interpolation, SIAM J. Numer. Anal. 7, pp. 112-124, 1970. | MR | Zbl

[4] J. H. Bramble and R. S. Hilbert, Bounds for a class of linear functionals with applications to Hermite interpolation, Numer. Math., 16, pp.362-369, 1971. | MR | Zbl

[5] J. H. Bramble and M. Zlamal, Triangular Elements in the finite element method, Math. Comp. 24, pp. 809-820, 1970. | MR | Zbl

[6] F. Brezzi, Sur une méthode hybride pour l'approximation du problème de la torsion d'une barre élastique Rend. Ist. Lombardo Sci. Lett. A, 108 (1974), 274-300. | MR | Zbl

[7] F. Brezzi, Sur la méthode des éléments finis hybrides pour le problème biharmonique. Num. Math. 24(1975) 103-131. | MR | Zbl

[8] F. Brezzi, On the existence uniqueness and approximation of saddle point problems arising from Lagrangian multipliers. R.A.I.R.O. 8-R2 (1974) 129-151. | Numdam | MR | Zbl

[9] P. G. Ciarlet, Quelques méthodes d'éléments finis pour le problème d'une plaque encastrée, Colloque IRIA sur « Méthodes de calcul scientifique et technique », Roquencourt (Paris) 17-21 déc. 1973. (To appear in Springer Verlag). | MR | Zbl

[10] P. G. Ciarlet, Sur l'élément de Clough et Tocher. (To appear). | Numdam | Zbl

[11] P. G. Ciarlet and P. A. Raviart, La méthode des éléments finis pour les problèmes aux limites elliptiques. (To appear).

[12] P. G. Ciarlet and P. A. Raviart, A mixed finite element method for the biharmonic equation, Symposium on Mathematical Aspect of Finite Elements in P.D.E., University of Wisconsin, Madison, April 01-03, 1974. | Zbl

[13] P. G. Ciarlet and P. A. Raviart, A nonconforming method for the plate problem. (To appear).

[14] P. G. Ciarlet and P. A. Raviart, General Lagrange and Hermite interpolation in R n with applications to finite element method, Arch. Rat. Mech. Anal. 46,pp. 177-189, 1972. | MR | Zbl

[15] J. F. Ciavaldini and J. C. Nedelec. (To appear).

[16] R. W. Clough and J. L. Tocher, Finite element stiffness matrices for analysis of plate in bending. Conference on Matrix Methods in Structural Mechanics, Wright Patterson A.F.B., Ohio, 1965.

[17] G. Fichera, Esistenza del minimo in un classico problema di calcolo delle variazioni, Rend. Acc. Nazionale Lincei, s. VIII, v. XI, fasc. 1-2, pp. 34-39, 1951. | MR | Zbl

[18] G. Fichera, Linear elliptic differential systems and eigenvalue problems, Lecture Notes, Springer Verlag, Berlin. 1965. | MR | Zbl

[19] B. Fraeijs De Veubeke, Displacements and equilibrium models in the finite element method, Stress Analysis (éd. by O. C. Zienkiewicz and G. S. Holister), chap. 9, Wiley, 1964.

[20] B. Fraeijs De Veubeke, Bending and stretching of plates, Conference on Matrix Methods in Structural Mechanics, Wright Patterson A.F.B., Ohio, 1965.

[21] B. Fraeijs De Veubeke, Variational principles and the patch test. (To appear on Internat. J. Numer. Methods Engrg., 8, 783-801, 1974. | MR | Zbl

[22] B. Fraeijs De Veubeke and O. C. Zienkiewicz, Strain-energy bounds in finite-element analysis by slab analogy, Journal of strain analysis, Vol. 2 N. 4, 1967.

[23] R. Glowinski, Approximations externes, par éléments finis de Lagrange d'ordre un et deux, du problème de Dirichlet pour l'opérateur biharmonique. Méthode itérative de résolution des problèmes approchés, Conference on Numerical Analysis, Royal Irish Academy, 1972. | Zbl

[24] B. M. Irons and A. Razzaque, 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), pp. 557-587, Academic Press, New York, 1972. | MR | Zbl

[25] C. Johnson, On the convergence ofsome mixed finite element methods inplate bending problems, Num. Math, 21 (1),43-62 (1973). | MR | Zbl

[26] C. Johnson, Convergence of another mixed finite element method for plate bending problems, Report N. 27, Department of Mathematics, Chalmers Institute of Technology and the University of Goteborg, 1972.

[27] P. Lascaux and P. Lesaint, Convergence de certains éléments finis non conformes pour le problème de la flexion des plaques minces. (To appear).

[28] J. L. Lions and E. Magenes, Non homogeneous boundary value problems and applications, I, II, Grund. B. 181-182, Springer-Berlin, 1970. | Zbl

[29] B. Mercier, Numerical solution of the biharmonic problem by mixed finite elements of class C°. Boll U.M.I., 4, 10, 1974. | MR | Zbl

[30] J. T. Oden, Some contributions to the mathematical theory of mixed finite element approximations, Tokyo Seminar on Finite Elements, 1973. | Zbl

[31] T. H. H. Pian, Hybrid Models, Int. Symp. on Numerical and Computer Methods in Structural Mechanics, Urbana, Illinois, Sept. 1971.

[32] T. H. H. Pian, Finite element formulation by variational principles with relaxed continuity requirements, The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (A. K. Aziz, Editor), Academic Press, New York, 1972. | MR | Zbl

[33] T. H. H. Pian and P. Tong, Basis of finite element methods for solid continua, Internat. J. Numer. Methods Engrg, Vol. I, 3-28, 1969. | Zbl

[34] T. H. H. Pian and P. Tong, A variational principle and the convergence of a finite element method based on assumed stress distribution, Int. J. Solids & Struct. 5, pp. 463-472, 1969. | Zbl

[35] T. H. H. Pian and P. Tong, Rationalization in Deriving element stiffness Matrix by assumed stress approach, Proceedings Second Conf. on Matrix Methods in Structural Mechanics, FFDL TR-68-150. Wright Patterson, AFB, Ohio, pp. 441-469, 1968.

[36] P. A. Raviart, Cours de troisième cycle, de l'Université de Paris VI, 1971-1972.

[37] P. A. Raviart, Hybrid finite element methods for solving 2nd order elliptic equations. Conference on Numerical Analysis, Royal Irish Academy, Dublin, July 29-August 2, 1974. | Zbl

[38] P. A. Raviart and J. M. Thomas, Hybrid finite element methods and 2nd order elliptic problems. (To appear.)

[39] G. Sander, Applications de la méthode des éléments finis à la flexion des plaques, Université de Liège, Fac. de Sci. Appl., Pubblic. N. 15, 1969.

[40] G. Strang, Approximation in the finite element method, Numer. Math., 19, pp. 81-98, 1972. | MR | Zbl

[41] G. Strang, Variational Crimes in the finite element method, The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (A. K. Aziz, Editor), pp. 689-710, Academic Press, NewYork, 1972. | MR | Zbl

[42] G. Strang and G. Fix, An Analysis of the Finite Element Method, Prentice Hall Englewood Cliffs, 1973. | MR | Zbl

[43] L. Tartar. (To appear.)

[44] S. Timoschenko, Theory of Plates and Shells, McGraw-Hill, New York, 1959. | JFM

[45] J. M. Thomas. (To appear.)

[46] O. C. Zienkiewicz, The finite element method in engineering Science, McGraw-Hill, London, 1971. | MR | Zbl

[47] M. Zlamal, On the finite element method, Numer. Math., 12, pp. 394-409, 1968. | MR | Zbl