Strict and practical bounds through a non-intrusive and goal-oriented error estimation method for linear viscoelasticity problems

Finite Elements in Analysis and Design

Volumn 45, Issue 4, 2009, Pages 251-262

  Chamoin, Ludovic ^a   Ladevèze, Pierre ^a,b  

^a CNRS   (France)

^b Advanced Computational Structural Mechanics ^*  (France)

Author keywords

Goal oriented error estimation; Handbook techniques; Non intrusive methods; Strict bounds; Verification

Indexed keywords

ELASTICITY; ERROR ANALYSIS; FINITE ELEMENT METHOD; HANDBOOKS; VISCOELASTICITY; VISCOSITY;

ADJOINT PROBLEMS; DISCRETIZATION; DISCRETIZATION ERRORS; DISSIPATION ERRORS; DUALITY TECHNIQUES; ERROR BOUNDS; FINITE ELEMENT CODES; FINITE-ELEMENT METHODS; GOAL-ORIENTED ERROR ESTIMATION; HIGH QUALITIES; LINEAR VISCOELASTICITIES; LOCAL ERROR ESTIMATIONS; NON-INTRUSIVE; NON-INTRUSIVE METHODS; PARTITION OF UNITIES; PRIMAL PROBLEMS; STRICT BOUNDS;

ESTIMATION;

EID: 60949100350     PISSN: 0168874X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.finel.2008.10.003     Document Type: Article

References (21)

1. Babuška I., and Rheinboldt W.C. A posteriori error estimates for the finite element method. Int. J. Numer. Methods Eng. 12 (1978) 1597
2. Ladevèze P., and Leguillon D. Error estimate procedure in the finite element method and application. SIAM J. Numer. Anal. 20 3 (1983) 485-509
3. Zienkiewicz O.C., and Zhu J.Z. A simple error estimator and adaptative procedure for practical engineering analysis. Int. J. Numer. Methods Eng. 24 (1987) 337-357
4. Paraschivoiu M., Peraire J., and Patera A.T. A posteriori finite element bounds for linear functional outputs of elliptic partial differential equations. Comput. Methods Appl. Mech. Eng. 150 (1997) 289-312
5. Prudhomme S., and Oden J.T. On goal-oriented error estimation for elliptic problems: application to the control of pointwise errors. Comput. Methods Appl. Mech. Eng. 176 (1999) 313-331
6. Ladevèze P., Rougeot P., Blanchard P., and Moreau J.P. Local error estimators for finite element linear analysis. Comput. Methods Appl. Mech. Eng. 176 (1999) 231-246
7. Stein E., Ohmnimus S., and Walhorn E. Local error estimates of fem for displacements and stresses in linear elasticity by solving local Neumann problems. Int. J. Numer. Methods Eng. 52 (2001) 727-746
8. Parès N., Bonet J., Huerta A., and Peraire J. The computation of bounds for linear-functional outputs of weak solutions to the two-dimensional elasticity equations. Comput. Methods Appl. Mech. Eng. 195 4-6 (2006) 406-429
9. Eriksson K., Estep D., Hansbo P., and Johnson C. Introduction to adaptive methods for partial differential equations. In: Isereles A. (Ed). Acta Numerica (1995), Cambridge University Press, Cambridge 105-159
10. Rannacher R., and Suttmeier F.T. A posteriori error control and mesh adaptation for finite element models in elasticity and elasto-plasticity. In: Ladevèze P., and Oden J.T. (Eds). Advances in Adaptative Computational Method in Mechanics (1998), Elsevier, Amsterdam 275-292
11. Chamoin L., and Ladevèze P. Bounds on history-dependent or independent local quantities in viscoelasticity problems solved by approximate methods. Int. J. Numer. Methods Eng. 71 12 (2007) 1387-1411
12. P. Ladevèze, Upper error bounds on calculated outputs of interest for linear and nonlinear structural problems, C. R. Acad. des Sci. Mec. Paris 334 (2006) 399-407.
13. Chamoin L., and Ladevèze P. A non-intrusive method for the calculation of strict and efficient bounds of calculated outputs of interest in linear viscoelasticity problems. Comput. Methods Appl. Mech. Eng. 197 9-12 (2008) 994-1014
14. Strouboulis T., Babuška I., and Copps E. The design and analysis of the generalized finite element method. Comput. Methods Appl. Mech. Eng. 181 (2000) 43-69
15. Ladevèze P., and Moës N. A new a posteriori error estimation for nonlinear time-dependent finite element analysis. Comput. Methods Appl. Mech. Eng. 157 (1998) 45-68
16. Ladevèze P., and Pelle J.-P. Mastering Calculations in Linear and Nonlinear Mechanics (2004), Springer, NY
17. Becker R., and Rannacher R. An optimal control approach to shape a posteriori error estimation in finite element methods. In: Isereles A. (Ed). Acta Numerica vol. 10 (2001), Cambridge University Press, Cambridge 1-120
18. Ladevèze P. Strict upper error bounds for calculated outputs of interest in computational structural mechanics. Comput. Mech. 42 2 (2008) 271-286
19. Mindlin R.D. Force at a point in the interior of a semi-infinite solid. J. Phys. 7 (1936) 195-202
20. Courant R., and Hilbert D. Methods of Mathematical Physics (1953), Interscience, New York
21. Sneddon I.N., and Hill R. Progress in Solid Mechanics (1964), North-Holland, Amsterdam