Conforming equilibrium finite element methods for some elliptic plane problems

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1. [1] D. J. ALLMAN, On compatible and equilibrium models with linear stresses for stretching of elastic plates, in [27]. Zbl0407.73059
2. [2] F. BREZZI, Non-standard finite elements for fourth order elliptic problems, in [27]. Zbl0411.41013
3. [3] G. R. BUSACKER and T. L. SAATY, Finite graphs and network : an introduction with applications, McGraw-Hill, New York, London, Sydney, 1965. Zbl0146.20104MR209176
4. [4] P. G. CIARLET, The finite element method for elliptic problems, North-Holland publishing company, Amsterdam, NewYork, Oxford, 1978. Zbl0383.65058MR520174
5. [5] G. DUVAUT and J. L. LIONS, Inequalities in mechanics and physics, Springer-Verlag, Berlin, Heidelberg, NewYork, 1976. Zbl0331.35002MR521262
6. [6] M. FORTIN, Approximation des fonctions à divergence nulle par la méthode des éléments finis, Proceedings of the Third International Conference on Numerical Methods in Fluid Mechanics, Paris, 1972, vol. 1, 99-103. Zbl0277.76024MR478666
7. [7] B. M. FRAEIJS DE VEUBEKE and M. HOGGE, Dual analysis for heat conduction problems by finite elements, Internat. J. Numer. Methods Energ. 5 (1972), 65-82 Zbl0251.65061
8. [8] V. GIRAULT and P. A. RAVIART, Finite element approximation of the Navier-Stokes equation, Springer-Verlag, Berlin, Heidelberg, New York, 1979. Zbl0413.65081MR548867
9. [9] R. GLOWINSKI and O. PIRONNEAU, On numerical methods for the Stokes problem, in [27]. Zbl0415.76024
10. [10] B. J. HARTZ and V. B. WATWOOD, An equilibrium stress field model for finite element solution of two-dimensional electrostatic problems, Internat. J. Solids and Structures 4 (1968), 857-873. Zbl0164.26201
11. [11] J. HASLINGER and I. HLAVACEK, Convergence of a finite element method based on the dual variational formulation, Apl. Mat. 21 (1976), 43-65. Zbl0326.35020MR398126
12. [12] I. HLAVACEK, Convergence of an equilibrium finite element model for plane elastostatics, Apl. Mat. 24 (1979), 427-457. Zbl0441.73101MR547046
13. [13] I. HLAVACEK, The density of solenoidal functions and the convergence of a dual finite element method, Apl. Mat. 25 (1980), 39-55. Zbl0424.65056MR554090
14. [14] C. JOHNSON, On the convergence of a mixed finite element method for plate bending problems, Numer. Math. 21 (1973), 43-62. Zbl0264.65070MR388807
15. [15] C. JOHNSON and B. MERCIER, Some equilibrium finite element methods for two-dimensional elasticity problems, Numer. Maht. 30 (1978), 103-116. Zbl0427.73072MR483904
16. [16] D. W. KELLY, Bounds on discretization error by special reduced integration of the Lagrange family of finite elements, Internat. J. Numer. Methods Energ. 15 (1980), 1489-1506. Zbl0438.73057MR595369
17. [17] M. KRIZEK, An equilibrium finite element method in three-dimensional elasticity, Apl. Mat. 27 (1982), 46-75. Zbl0488.73072MR640139
18. [18] B. MERCIER, Topics in finite element solution of elliptic problems, Springer-Verlag, Berlin, Heidelberg, New York, 1979. Zbl0445.65100
19. [19] J. NECAS, Les méthodes directes en théorie des équations elleptiques, Academia, Prague, 1967. MR227584
20. [20] J. NECAS and I. HLAVACEK, Mahtematical theory of elastic and elasto-plastic bodies : an introduction, Elsevier Scientific Publishing Company, Amsterdam, Oxford, New York, 1981. Zbl0448.73009MR600655
21. [21] A. R. S. PONTER, The application of dual minimum theorems to the finite element solution of potential problems with special reference to seepage, Internat. J. Numer. Methods Energ. 4 (1972), 85-93. Zbl0254.76095MR297211
22. [22] G. SANDER, Application of the dual analysis principle , Proceedings of the IUTAM Symposium on High Speed Computing of Elastic Structures, Congrès et Colloques de l'Université de Liège (1971), 167-207. 
23. [23] R. TEMAM, Navier-Stokes equations North-Holland publishing company, Amsterdam, New York, Oxford, 1977. Zbl0426.35003MR603444
24. [24] J. M. THOMAS, Sur l'analyse numérique des méthodes d'éléments finis hybrides et mixtes, Thesis, Université Paris VI, 1977. 
25. [25] J. M. THOMAS and M. AMARA, Approximation par éléments finis équilibre du système de l'élasticité linéaire, C.R. Acad. Sc. Paris, t. 286 (1978), 1147-1150. Zbl0395.73011MR495556
26. [26] J. M. THOMAS and M. AMARA, Equilibrium finite elements for the linear elastic problem, Numer. Math. 33 (1979), 367-383. Zbl0401.73079MR553347
27. [27] Energy methods in finite element analysis, John Wiley & Sons Ltd., Chichester, New York, Brisbane, Toronto, 1979. MR536995

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