## Convergence of a finite element method based on the dual variational formulation.(English)Zbl 0326.35020

### MSC:

 35J20 Variational methods for second-order elliptic equations 35A35 Theoretical approximation in context of PDEs 35B45 A priori estimates in context of PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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### References:

 [1] B. Fraeijs de Veubeke: Displacement and equilibrium models in the finite element method. Stress Analysis by O.C. Zienkiewicz and G. Holister, J. Wiley, 1965, 145-197. [2] B. Fraeijs de Veubeke O. C. Zienkiewicz: Strain energy bounds in finite-element analysis by slab analogies. J. Strain Analysis 2, (1967) 265 - 271. [3] V. B., Jr. Watwood B. J. Hartz: An equilibrium stress field model for finite element solution of two-dimensional elastostatic problems. Int. J. Solids Structures 4, (1968), 857-873. · Zbl 0164.26201 [4] B. Fraeijs de Veubeke M. Hogge: Dual analysis for heat conduction problems by finite elements. Int. J. Numer. Meth. Eng. 5, (1972), 65 - 82. · Zbl 0251.65061 [5] J. P. Aubin H. G. Burchard: Some aspects of the method of the hypercircle applied to elliptic variational problems. Numer. sol. Part. Dif. Eqs. II, SYNSPADE (1970), 1 - 67. [6] J. Vacek: Dual variational principles for an elliptic partial differential equation. Apl. mat. 21 (1976), 5-27. · Zbl 0345.35035 [7] I. Hlaváček: On a conjugate semi-variational method for parabolic equations. Apl. mat. 18 (1973), 434-444. [8] F. Grenacher: A posteriori error estimates for elliptic partial differential equations. Inst. Fluid Dynamics and Appl. Math., Univ. Maryland, TN-BN-T 43, July 1972. [9] W. Prager J. L. Synge: Approximations in elasticity based on the concept of function space. Quart. Appl. Math. 5 (1947), 241 - 269. · Zbl 0029.23505 [10] J. Nečas: Les méthodes directes en théorie des équations elliptiques. Academia, Prague 1967. · Zbl 1225.35003 [11] I. Hlaváček: Variational principles in the linear theory of elasticity for general boundary conditions. Apl. mat. 12 (1967), 425-448. · Zbl 0153.55401 [12] J. Haslinger J. Hlaváček: Convergence of a dual finite element method in $$R_n$$. CMUC 16 (1975), 469-485. · Zbl 0321.65060 [13] H. Gajewski: On conjugate evolution equations and a posteriori error estimates. Proceedings of Internal. Summer School on Nonlinear Operators held in Berlin, 1975. · Zbl 0367.35051
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