Dual analysis with general boundary conditions. (English) Zbl 0851.73057

Debongnie, J. F.; Zhong, H. G.; Beckers, P.

Comput. Methods Appl. Mech. Eng. 122, No. 1-2, 183-192 (1995).

This paper presents a reexamination of the dual error measure by a way which avoids any use of upper and lower bounds of the energy. It is found that such an error measure holds whatever the boundary conditions are. Furthermore, it is not necessary to obtain the approximate solutions by a Rayleigh-Ritz process, so that the second analysis, which seemed necessary in the original dual analysis concept, may be replaced by any admissible approximation. This implies the possibility of a dual measure at a simple post-processor level.

MSC:

74S05	Finite element methods applied to problems in solid mechanics
74B05	Classical linear elasticity

Keywords:

dual error measure

References:

[1]	Fraeijs de Veubeke, B., Sur certaines inégalités fondamentales et leur généralisation dans la théorie des bornes supérieures et inférieures en élasticité, Revue Universelle des Mines, XVII, n °5 (1961) · Zbl 0108.37203
[2]	Fraeijs de Veubeke, B., Upper and lower bounds in matrix structural analysis, (AGARDograph 72 165 (1964), Pergamon Press) · Zbl 0131.22903
[3]	Fraeijs de Veubeke, B., Duality in structural analysis by finite elements, NATO advanced studies institute—Lecture series on finite element methods in continuum mechanics (1971), Lisbon · Zbl 0283.73029
[4]	Sander, G., Application of the dual analysis principle, (Proc. IUTAM. Proc. IUTAM, Liège, Belgium (August, 1970))
[5]	Beckers, P., Les fonctions de tension dans la méthode des éléments finis, (Doctoral thesis (1972), University of Liège: University of Liège Belgium)
[6]	Geradin, M., Computational efficiency of equilibrium models in eigenvalue analysis, (Proc. IUTAM. Proc. IUTAM, Liège, Belgium (August, 1970)) · Zbl 0225.65050
[7]	Debongnie, J. F., A general theory of dual error bounds by finite elements, (report LMF/D5 (1983), University of Liège: University of Liège Belgium) · Zbl 0393.73097
[8]	Ladeveze, P., Comparison de Modèles de milieux continus, (Doctoral thesis (1975), University P & M Curie: University P & M Curie Paris)
[9]	Ladeveze, P.; Leguillon, D., Error estimate procedure in the finite element method and applications, SIAM J. Numer. Anal., 20, 3, 483-509 (1983) · Zbl 0582.65078
[10]	Ladeveze, P.; Pelle, J. P.; Rougeot, P., Error estimation and mesh optimization for classical finite elements, Engrg. Comput., 8, 69-80 (1991)
[11]	Ainsworth, M.; Oden, J. T., A procedure for a posteriori error estimation for h-p finite element methods, Comput. Methods Appl. Mech. Engrg., 101, 73-96 (1992) · Zbl 0778.73060
[12]	Clough, R. W.; Felippa, C. A., A refined quadrilateral element for analysis of plate bending, (Proc. 2nd. Conf. Matrix Methods in Structure Mechanics (1968), Air Force Inst. of Tech., Wright Patterson Air Force Base: Air Force Inst. of Tech., Wright Patterson Air Force Base Ohio)
[13]	Morley, L. S.D., The triangular equilibrium element in the solution of plate bending problems, Aero Quart., 19, 149-169 (1968)
[14]	Fraeijs de Veubeke, B.; Zienkiewicz, O. C., Strain energy bounds in finite element analysis by the slab analogy, J. Strain Anal. Inst. of Mechanical Engrg., 2, 4 (1967)
[15]	Zhong, H. G., Estimateurs d’erreur a posteriori et adaptation de maillages dans la méthode des éléments finis, (Doctoral thesis (1991), University of Liège: University of Liège Belgium)