On the Existence, Uniqueness and Approximation of Saddle-Point Problems Arising from Lagrangian Multipliers

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1. [1] J.P. Aubin - "Approximation of elliptic boundary-value problems" Wiley-New York, (1972). Zbl0248.65063MR478662
2. [2] J.P. Aubin - "Cours d'optimisation" - Université de Paris IX Dauphine1973-1974). 
3. [3] J.P. Babuska - "Error bound for the finite element method" - Num. Math.16, 322-333 (1971) Zbl0214.42001MR288971
4. [4] I. Babuska - "The finite element method with Lagrangian multipliers" Num. Math.20, 179-192 (1973). Zbl0258.65108MR359352
5. [5] F. Brezzi - "Sur la méthode des élément finis hybrides pour le problème biharmonique" (submittend to Num. Math.) Zbl0316.65029
6. [6] F. Brezzi - "Sur une méthode hybride pour l'approximation du problème de la torsion d'une barre élastique" (to appear on Ist. Lombardo Accad. Sci. Lett. Rend. A). Zbl0351.73081MR378556
7. [7] F. Brezzi - "Sur l'existence, unicité et approximation numérique de problèmes de point de selle" C.R. Acad. Sc.Paris, Serie A, 278 (18 mars 1974), 839-842, (1974) Zbl0301.65031MR338867
8. [8] F. Brezzi- L.D. Marini - "On the numerical solution of plate bending problems by hybrid methods" (to appear on "Pubblicazioni del Laboratorio di Analisi Numerical del C.N.R., Pavia. Zbl0322.73048
9. [9] P.G. Ciarlet- P.A. Raviart - "General Lagrange and Hermite interpolation in $R^n$ with applications to finite element methods" Arch. Rat. Mech. Anal., 46, 177-199 (1972). Zbl0243.41004MR336957
10. [10] P.G. Ciarlet- P.A. Raviart - "The combined effect of curved boundaries and numerical integration in isoparametric finite element methods". The Math. Found. of the F.E.M.(ed. by A.K.AZIZ). Academic Press1972. Zbl0262.65070MR421108
11. [11] M. Crouzeix- P.A. Raviart - "Conforming and Nonconforming Finite Element methods for Solving the Stationary Stokes Equations. I(to appear). Zbl0302.65087MR343661
12. [12] B. Fraeijs de Veubeke - "Upper and lower bounds in matrix structural analysis" AGARDograph72, Pergamon, 1964. Zbl0131.22903
13. [13] B. Fraeijs de Veubeke - "Displacements and equilibrium models in the finite element method" - Stress Analysis (ed. by O. C. Zienkiewicz and G.S. Holister) ch.9 - Wiley, 1964. Zbl1065.74625
14. [14] B. Fraeijs de Veubeke - "Bending and Stretching of plates". Proc. Conf. Matrix Method in Structural Mech., Air Force Technical Report AFF DL-TR-66-80, Nov. 1966. 
15. [15] B. Fraeijs de Veubeke - "Variational principles and the patch-test" (to appear on Int. J. Numerical Meth. in Eng.) Zbl0284.73043MR375911
16. [16] B. Fraeijs de Veubeke- O.C. Zienkiewicz - "Strain energy bounds in finite-element analysis by slab analogy". Journal of Strain Analysis2, 4, 265-271 (1967). 
17. [17] B.M. Irons- A. RAZZAQUE - "Experience with patch-test for convergence of finite elements". The Math. Found of the F.E.M. (ed. by A.K. AZIZ). Academic Press1972. Zbl0279.65087MR423839
18. [18] C. Johnson -"On the convergence of a Mixed Finite Element Method for Plate Bending Problems"- Num. Math.21 , 43-62 (1973). Zbl0264.65070MR388807
19. [19] C. Johnson -"Convergence of another mixed finite-element method for plate bending problems" - Chalmers Institute of Technology No. 1972-27. Zbl0264.65070MR388807
20. [20] F. Kikuci- Y. Ando - "On the convergence of a mixed finite element scheme for plate bending" - Nucl. Eng. and Design., 24, 357-373 (1973) . 
21. [21] Lascaux- P. Sesaint - (to appear), MR2816384
22. [22] J.L. Lions- E. Magenes - "Non homogeneous boundary value problems and applications" vol.1, 2 - Grundlehren B.181,182 - Springer1971. Zbl0227.35001
23. [23] B. Mercier - "Numerical solution of the biharmonic problem by mixed finite elements of class $C^0$" (to appear in Boll. U.M.I.(1974) Zbl0332.65058MR378442
24. [24] T.H.H. Pian- P. TONG - "A variational principle and the convergence of a finite-element method based on assumed stresses distribution"- Inst. J. Solid Structures, 5, 463-472 (1969). Zbl0167.52805
25. [25] T.H.H. Pian- P. Tong - "Basis of finite element methods for solid continua" Inz. J. for Numerical Math, in Eng. 13-28 (1969). Zbl0252.73052
26. [26] P.A. Raviart - "Méthode des éléments finis" Cours1972-1973 à  l'Université de Paris VI. 
27. [27] P.A. Raviart- J.M. Thomas - (to appear) 
28. [28] G. Sander - "Application of the dual analysis principle" - Proceedings of IUTAM - Liege Aug. 1970 
29. [29] G. Sander - "Application de la méthode des éléments finis à la flexion des plaques" - Coll. Publ. Fac. Se. Appl. Univ." Liège n.15 (1969). 
30. [30] G. Strang - "Variationalcrimes in the finite element methods" -The Math. Found, of the F.E.M. (ed. by A.K. AZIZ) Academic Press (1972). Zbl0264.65068MR413554
31. [31] G. Strang - FIX - "An analysis of the finite elements method" Prentice Hall-New York, 1973. Zbl0356.65096MR443377
32. [32] J.M. Thomas (to appear) 
33. [33] K. Yosida - "Functional Analysis" Grundlehren B.123 - Springer, 1965. Zbl0435.46002
34. [34] O.C. Zienkiewicz - "The finite element methods in engineering science" Mc Graw-Hill (1971). Zbl0237.73071MR315970