Local error estimators for finite element linear analysis

Computer Methods in Applied Mechanics and Engineering

Volumn 176, Issue 1-4, 1999, Pages 231-246

  Ladeveze P ^a   Rougeot, Ph ^a   Blanchard, P ^b   Moreau, J P ^b  

^a CNRS   (France)

^b Aerospatiale Etablissement des M   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ERROR ANALYSIS; PROBLEM SOLVING;

ERROR ESTIMATION;

FINITE ELEMENT METHOD;

EID: 0032651556     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(98)00339-9     Document Type: Article

References (20)

1. [1] P. Ladevèze and J.T. Oden, Advances in Adaptive Computational Methods in Mechanics (Elsevier, 1998).
2. [2] I. Babuška, T. Strouboulis, C.S. Upadhyay and S.K. Gangaraj, A posteriori estimation and adaptive control of the pollution error in the h-version of the finite element method, Int. J. Numer. Methods Engrg. 38 (1995) 4207-4235.
3. [3] I. Babuška, T. Strouboulis, S.K. Gangaraj, K. Copps and D.K. Datta, A posteriori estimation of the error estimate, in: P. Ladevèze and J.T. Oden, eds., Advances in Adaptive Computational Methods (Elsevier, 1998) 155-197.
4. [4] J. Peraire and A. Patera, Bounds for linear-functional outputs of coercive partial differential equations: local indicators and adaptive refinement, in: P. Ladevèze and J.T. Oden, eds., Advances in Adaptive Computational Methods (Elsevier, 1998) 199-216.
5. [5] M. Paraschivoiu, J. Peraire and A. Patera, A posteriori finite element bounds for linear-functional outputs of elliptic partial differential equation, Comput. Methods Appl. Mech. Engrg. 150 (1997) 289-312.
6. [6] R. Beckers and R. Rannacher, A feedback approach to error control in finite element methods: Basic analysis and examples, East-West J. Numer. Math. 4 (1996) 237-264.
7. [7] R. Rannacher and F.T. Suttmeier, A feedback approach to error control in finite element methods: Application to linear elasticity, Comput. Mech. 19 (1997) 433-446.
8. [8] P. Ladevèze, Une théorie pour l'estimation des erreurs locales dans les calculs par éléments finis, Technical Note YX/ST 126045, Aérospatiale, 1998.
9. [9] P. Ladevèze, La méthode d'évaluation d'erreur en relation de comportement appliquée à la M.E.F.: qualité et amélioration, Technical Report 153, L.M.T. Cachan, 1994.
10. [10] P. Ladevèze and P. Rougeot, New advances in a posteriori error on constitutive relation in f.e. analysis, Comput. Methods Appl. Mech. Engrg. 150 (1997) 239-249.
11. [11] P. Ladevèze, Nouvelles procédures d'estimations d'erreur relative à la méthode des éléments finis, in: Proc. Journées Eléments finis, Rennes, 1977.
12. [12] P. Ladevèze and D. Leguillon, Error estimate procedure in the finite element method and application, SIAM J. Numer. Anal. 20(3) (1983) 485-509.
13. [13] P. Ladevèze, G. Coffignal and J.P. Pelle, Accuracy of elastoplastic and dynamic analysis, in: I. Babuška, J. Gago, E.R. de A. Oliveira and O.C. Zienkiewicz, eds., Accuracy Estimates and Adaptive Refinements in Finite Element Computations (J. Wiley, 1986) 181-203.
14. [14] L. Gallimard, P. Ladevèze and J.P. Pelle. Error estimation and adaptivity in elastoplasticity, Int. J. Numer. Methods Engrg. 39 (1996) 189-217.
15. [15] P. Ladevèze and N. Moës, Adaptive control for time-dependent nonlinear finite element analysis, Advances in Finite Element Technology, (Civil-Comp Press, Edinburgh, 1996) 79-92.
16. [16] M. Ainsworth and J.T. Oden, A posteriori error estimation in finite element analysis. Mathematics and Computer Science Technical Report 14, University of Leicester, UK, 1995.
17. [17] 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.
18. [18] O.C. Zienkiewicz and J.Z. Zhu, The superconvergent patch recovery and a posteriori error estimates, Part 2: Error estimates and adaptivity. Int. J. Numer. Methods Engrg. 33 (1992) 1365-1382.
19. [19] P. Labbé and A. Garon, A robust implementation of Zienkiewicz and Zhu's local patch recovery method, Communications in Num. Methods Engrg. 11 (1995) 427-434.
20. [20] M. Paraschivoiu and A. Patera, A hierarchical duality approach to bounds for the outputs of partial differential equations, Comput. Methods Appl. Mech. Engrg. 158 (1998) 389-407.