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All issues Volume 11 / No 3-4 (Mai-Août 2010) Mécanique & Industries, 11 3-4 (2010) 249-254 References
Open Access
Issue
Mécanique & Industries
Volume 11, Number 3-4, Mai-Août 2010
Giens 2009
Page(s) 249 - 254
DOI https://doi.org/10.1051/meca/2010049
Published online 20 December 2010
  1. M. Ainsworth, J.T. Oden, A posteriori error estimation in finite element analysis,Pure and Applied Mathematics, Wiley-Interscience, 2000 [Google Scholar]
  2. N.E. Wiberg, P. Díez, Adaptive modeling and simulation, Comput. Methods Appl. Mech. Eng. 195 (2006) 205–480 [CrossRef] [Google Scholar]
  3. P. Ladevèze, J.-P. Pelle, Mastering calculations in linear and nonlinear mechanics, Mechanical Engineering, Springer, 2005 [Google Scholar]
  4. P. Ladevèze, Upper error bound on calculated outputs of interest for linear and nonlinear structural problems, C. R. Mécanique 334 (2006) 399–407 [Google Scholar]
  5. L. Chamoin, P. Ladevèze, Bounds on history-dependent or independent local quantities in viscoelasticity problems solved by approximate methods, Int. J. Numer. Meth. Eng. 71 (2007) 1387–1411 [CrossRef] [Google Scholar]
  6. P. Ladevèze, L. Chamoin, E. Florentin, A new non-intrusive technique for the construction of admissible stress fields in model verification, Comput. Methods Appl. Mech. Eng. 199 (2010) 766–777 [CrossRef] [Google Scholar]
  7. O.C. Zienkiewicz, J.Z. Zhu, A simple error estimator and adaptive procedure for practical engineering analysis, Int. J. Numer. Meth. Eng. 24 (1987) 337–357 [Google Scholar]
  8. I. Babuška, W.C. Rheinboldt, Error estimates for adaptive finite element computations, SIAM J. Numer. Anal. 15 (1978) 736–755 [CrossRef] [MathSciNet] [Google Scholar]
  9. P. Ladevèze, D. Leguillon, Error estimate procedure in the finite element method and applications, SIAM J. Numer. Anal. 20 (1983) 485–509 [CrossRef] [MathSciNet] [Google Scholar]
  10. J.Z. Zhu,A posteriori error estimation – the relationship between different procedures, Comput. Methods Appl. Mech. Eng. 150 (1997) 411–422 [CrossRef] [Google Scholar]
  11. H.-W. Choi, M. Paraschivoiu, Adaptive computations of a posteriori finite element output bounds: a comparison of the “hybrid-flux” approach and the “flux-free” approach, Comput. Methods Appl. Mech. Eng. 193 (2004) 4001–4033 [CrossRef] [Google Scholar]
  12. N. Parés, P. Díez, A. Huerta, Subdomain-based flux-free a posteriori error estimators, Comput. Methods Appl. Mech. Eng. 195 (2006) 297–323 [CrossRef] [Google Scholar]
  13. C. Carstensen, S.A. Funken, Fully reliable localized error control in the FEM, SIAM J. Sci. Comput. 21 (1999-2000) 1465–1484 [Google Scholar]
  14. L. Machiels, Y. Maday, A.T. Patera, A “flux-free” nodal Neumann subproblem approach to output bounds for partial differential equations, C.-R. Acad. Sci. Ser. I – Math. 330 (2000) 249–254 [Google Scholar]
  15. P. Morin, R.H. Nochetto, K.G. Siebert, Local problems on stars: a posteriori error estimators, convergence, and performance, Math. Comp. 72 (2003) 1067–1097 [CrossRef] [MathSciNet] [Google Scholar]
  16. S. Prudhomme, F. Nobile, L. Chamoin, J.T. Oden, Analysis of a subdomain-based error estimator for finite element approximations of elliptic problems, Numer. Methods Partial Differ. Eqs. 20 (2004) 165–192 [CrossRef] [Google Scholar]
  17. J.P. Moitinho de Almeida, E.A.W. Maunder, Recovery of equilibrium on star patches using a partition of unity technique, Int. J. Numer. Meth. Eng. 2008, submitted [Google Scholar]
  18. A.M. Sauer-Budge, J. Bonet, A. Huerta, J. Peraire, Computing bounds for linear functionals of exact weak solutions to Poisson’s equation, SIAM J. Numer. Anal. 42 (2004) 1610–1630 [CrossRef] [MathSciNet] [Google Scholar]
  19. N. Parés, J. Bonet, A. Huerta, J. Peraire, The computation of bounds for linear-functional outputs of weak solutions to the two-dimensional elasticity equations, Comput. Methods Appl. Mech. Eng. 195 (2006) 406–429 [CrossRef] [Google Scholar]
  20. N. Parés, P. Díez, A. Huerta, Bounds of functional outputs for parabolic problems. Part I: Exact bounds of the discontinuous Galerkin time discretization, Comput. Methods Appl. Mech. Eng. 197 (2008) 1641–1660 [Google Scholar]
  21. N. Parés, P. Díez, A. Huerta, Bounds of functional outputs for parabolic problems. Part II: Bounds of the exact solution, Comput. Methods Appl. Mech. Eng. 197 (2008) 1661–1679 [Google Scholar]
  22. R. Cottereau, P. Díez, A. Huerta, Strict error bounds for linear solid mechanics problems using a subdomain-based flux-free method, Comp. Mech. 44 (2009) 533–547 [CrossRef] [Google Scholar]
  23. R. Becker, R. Rannacher, An optimal control approach to shape a posteriori error estimation in finite element methods, Acta Numerica 10 (2001) 1–102 [Google Scholar]
  24. S. Prudhomme, J.T. Oden, On goal-oriented error estimation for elliptic problems: application to the control of pointwise errors, Comput. Methods Appl. Mech. Eng. 176 (1999) 313–331 [Google Scholar]
  25. J.J. Moreau, Fonctionnelles convexes, Cours du Collège de France, 1966 [Google Scholar]
  26. M. Paraschivoiu, J. Peraire, A.T. Patera, A posteriori finite element bounds for linear-functional outputs of elliptic partial differential equations, Comput. Methods Appl. Mech. Eng. 150 (1997) 23–50 [Google Scholar]

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