Previous |  Up |  Next


An "equilibrium model" with piecewise linear polynomials on triangular clements applied to the solution of a mixed boundary value problem for a second order elliptic equation is studied. The procedure is proved to be second order correct in $h$ (the maximal side in the triangulation) provided the exact solution is sufficiently smooth.
[1] B. Fraeijs de Veubeke: Displacement and equilibrium models in the finite element method. Stress Analysis, ed. 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. 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. 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. MR 0285136
[6] J. Vacek: Dual variational principles for an elliptic partial differential equation. Apl. mat. 21 (1976), 5-27. MR 0412594 | Zbl 0345.35035
[7] I. Hlaváček: On a conjugate semi-variational method for parabolic equations. Apl. mat. 18 (1973), 434-444. MR 0404858
[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. DOI 10.1090/qam/25902 | MR 0025902
[10] J. Nečas: Les méthodes directes en théorie des équations elliptiques. Academia, Prague 1967. MR 0227584
[11] I. Hlaváček: Variational principles in the linear theory of elasticity for general boundary conditions. Apl. mat. 12 (1967), 425-448. MR 0231575
[12] J. Haslinger J. Hlaváček: Convergence of a dual finite element method in $R_n$. CMUC 16 (1975), 469-485. MR 0386303
[13] H. Gajewski: On conjugate evolution equations and a posteriori error estimates. Proceedings of Internal. Summer School on Nonlinear Operators held in Berlin, 1975.
Partner of
EuDML logo