A new a posteriori error estimation for nonlinear time-dependent finite element analysis

Computer Methods in Applied Mechanics and Engineering

Volumn 157, Issue 1-2, 1998, Pages 45-68

  Ladevèze, Pierre ^a   Moës, Nicolas ^a  

^a CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ERROR ANALYSIS; FINITE ELEMENT METHOD; ITERATIVE METHODS; NONLINEAR EQUATIONS; PROBLEM SOLVING; VISCOPLASTICITY;

CONSTITUTIVE LAW ERROR;

STRUCTURAL ANALYSIS;

EID: 0032046356     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(97)00212-0     Document Type: Article

References (32)

1. [1] J. Lemaitre and J.L. Chaboche, Mechanics of Solid Materials (Cambridge University Press, Cambridge, 1990).
2. [2] P. Ladevèze, Les bases de la méthode de l'erreur en relation de comportement pour le contrôle des calculus éléments finis: Les travaux des années 1975. Rapport interne 163, LMT, Ecole Normale Supérieure de Cachan, 1995.
3. [3] P. Ladevèze, J.P. Pelle and P. Rougeot, Error estimation and mesh optimization for classical finite element, Engrg. Comput. 8 (1991) 69-80.
4. [4] I. Babuska and W.C. Rheinboldt, A posteriori estimates for the finite element method, Int. J. Numer. Methods Engrg. 12 (1978) 1597-1615.
5. [5] I. Babuska and W.C. Rheinboldt, Adaptive approaches and reliability estimators in finite element analysis, Comput. Methods Applied Mech. Engrg. 17/18 (1979) 519-540.
6. [6] D.W. Kelly, J. Gago, O.C. Zienkiewicz and I. Babuska, A posteriori error analysis and adaptative processes in finite element method. Part 1: Error analysis, Int. J. Numer. Methods Engrg. 19 (1983) 1593-1619.
7. [7] J. Gago, D.W. Kelly, O.C. Zienkiewicz and I. Babuska, A posteriori error analysis and adaptative processes in finite element method. Part 2: Adaptative mesh refinement, Int. J. Numer. Methods Engrg. 19 (1983) 1921-1656.
8. [8] J.T. Oden, L. Demkowicz, W. Rachoẃicz and T.A. Westermann, Toward a universal h-p adaptative finite element strategy, Part 2: A posteriori error estimation, Comput. Methods Appl. Mech. Engrg. 77 (1989) 113-180.
9. [9] O.C. Zienkiewicz and J.Z. Zhu, A simple error estimator and adaptative procedure for practical engineering analysis, Int. J. Numer. Methods Engrg. 24 (1987) 337-357.
10. [10] O.C. Zienkiewicz and J.Z. Zhu, The superconvergent patch recovery and a posteriori error estimates, Part 1: The recovery technique, Int. J. Numer. Methods Engrg. 33 (1992) 1331-1364.
11. [11] O.C. Zienkiewicz and J.Z. Zhu, The superconvergent patch recovery and a posteriori error estimates, Part 2: Error estimates and adaptativity, Int. J. Numer. Methods Engrg. 33 (1992) 1365-1382.
12. [12] B. Fraeijs de Veubeke, Displacement and equilibrium models in the finite element method, in: O.C. Zienkiewicz, ed., Stress Analysis Chap. 9 (John Wiley, 1965).
13. [13] J.F. Debongnie, H.G. Zhong and P. Beckers, Dual analysis with general boundary conditions, Comput. Methods. Appl. Mech. Engrg. 122 (1995) 183-192.
14. [14] I. Babuska, T. Strouboulis, C.S. Upadhyay, S.K. Gangaraj and K. Copps, Validation of a posteriori error estimators by numerical approach, Int. J. Numer. Methods Engrg. 37 (1994) 1073-1123.
15. [15] I. Babuska, T. Strouboulis, S.K. Gangaraj and C.S. Upadhyay, Pollution-error in the h-version of the finite-element method and the local quality of a-posterior error estimators, Finite Elements Anal. Des. 17 (1994) 273-321.
16. [16] I. Babuska, T. Strouboulis, S.K. Gangaraj and C.S. Upadhyay, Validation of recipes for the recovery of stresses and derivatives by a computer-based approach, Math. Comput. Model. 20 (1994) 45-89.
17. [17] I. Babuska and W.C. Rheinboldt, Computational error estimates and adaptative processes for some nonlinear structural problems, Comput. Methods Appl. Mech. Engrg. 34 (1982) 895-937.
18. [18] C. Johnson and P. Hansbo, Adaptative finite element methods in computational mechanics, Comput. Methods Appl. Mech. Engrg. 101 (1992) 143-181.
19. [19] J.M. Bass and J.T. Oden, Adaptative finite element methods for a class of evolution problems in viscoplasticity, Int. J. Engrg. Sci. 25(6) (1987) 623-653.
20. [20] O.C. Zienkiewicz, Y.C. Liu and G.C. Huang, Error estimation and adaptativity in flow formulation for forming problems, Int. J. Numer. Methods Engrg. 25 (1988) 23-42.
21. [21] B. Tie and D. Aubry, Error estimates, h adaptative strategy and hierarchical concept for non linear finite element method, in: Ch. Hirsch et al., eds., Numerical Methods in Engineering '92 (Elsevier Science Publishers, 1992) 17-24.
22. [22] P. Ladevèze, Sur une famille d'algorithmes en mécanique des structures, Compte-Rendus de l'Académie des Sciences, Série II 300 (1985) 41-44.
23. [23] P. Ladevèze, G. Coffignal and J.P. Pelle, Accuracy of elastoplastic and dynamic analysis, in: I. Babuska, J. Gago, E. Oliveira and O.C. Zienkiewicz, eds., Accuracy Estimates and Adaptative Refinements in Finite Element Computations (J. Wiley, 1986) 181-203.
24. [24] L. Gallimard, P. Ladevèze and J.P. Pelle, Error estimation and adaptativity in elastoplasticity, Int. J. Numer. Methods Engrg. 39 (1996) 189-217.
25. [25] P. Ladevèze, La méthode à grand incrément de temps pour l'analyse de structures à comportement non linéaires décrit par variables internes, Compute-Rendus de l'Académie des Sciences, Série II 309(11) (1989) 1095-1099.
26. [26] P. Ladevèze, Mécanique non linéaire des structures. Nouvelle Approache et Méthodes de Calcul Non Incrémentales (Hermes, 1996).
27. [27] G. de Saxcé, Une généralisation de l'inégalité de Fenchel et ses applications aux lois constitutives, Compte-Rendus de l'Académie des Sciences, Série II 314 (1992) 125-129.
28. [28] A. Berga and G. Saxcé, Elastoplastic finite element analysis of soil problems with implicit standard material constitutive laws, Revue européenne de éléments Finis 3(3) (1994) 411-456.
29. [29] G. Duvaut and J.L. Lions, Les Inéquations en Mécanique et en Physique (Dunod, 1972).
30. [30] P. Ladevèze, Nouvelles procédures d'estimations d'erreur relative à la méthode des éléments finis, in: Proc. Journées Eléments Finis, Rennes, 1977.
31. [31] W. Prager and J.L. Synge, Approximation in elasticity based on the concept of functions space, Quart. Appl. Math. 5 (1947) 261-269.
32. [32] P. Ladevèze, La maîtrise des modèles en mécanique des structures, Revue européenne de éléments finis 1 (1992) 9-30.