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


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
Full Text: DOI EuDML


[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. · doi:10.1243/03093247V024265
[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 · doi:10.1016/0020-7683(68)90083-8
[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 · doi:10.1002/nme.1620050107
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.