7. Bibliography#

      1. Ciarlet: The finite element methods for elliptic problems. North Holland, 1978.

    1. Strang & G.J. Fix: An Analysis of the Finite Element Method. Prentice-Hall, 1973.

    1. Babuška and W. Rheinboldt: « A Posteriori Error Estimates for the Finite Element Method », International Journal For Numerical Methods In Engineering, (12), 1978, pp.1597-1615.

  4. O.C. Zienkiewicz & J.Z. Zhu: A simple error estimator and adaptive procedure for practical engineering analysis. International Journal for Numerical Methods in Engineering, 24, pp.337-357, 1987.

    1. Ladevèze: « Comparison of continuous media models », Pierre and Marie Curie University - Paris VI, 1975.

    1. Verfürth: A review of a posteriori error estimation techniques for elasticity problems. Computer Methods in Applied Mechanics and Engineering, 176, pp.419-440, 1999.

    1. Ainsworth & J.T. Oden: A posteriori error estimation in finite element analysis. Computer Methods in Applied Mechanics and Engineering, 142, pp.1-88, 1997.

    1. Ladevèze & J.P. Pelle: Mastering Calculations in Linear and Nonlinear Mechanics, Springer NY, 2004.

    1. Ramm, E. Rank, R. Rannacher, S. K., S. K., E. Stein, E. Stein, G. Wendland, W. Wittum, P. Wriggers & W. Wunderlich: Error-controlled adaptive finite elements in solid mechanics. Stein (eds.), Wiley, 2003.

    1. Grätsch & K. Bathe: A posteriori error estimation techniques in practical finite element analysis. Computers and Structures, 83, pp.235-265, 2005.

    1. Strouboulis & K. A. Haque: Recent experiences with error estimation and adaptivity, Part II: Error estimation for h-adaptive approximations on grids of triangles and quadrilaterals. Computer Methods in Applied Mechanics and Engineering, 100, pp.359-430, 1992.

    1. Babuška, T. Strouboulis, A. Mathur, A. Mathur & C. Upadhyay: Pollution-error in the h-version of the finite-element method and the local quality of a-posteriori error estimators. Finite Elements in Analysis and Design, 17, pp.273-321, 1994.

    1. Wiberg & F. Abdulwahab: Patch recovery based on superconvergent derivatives and equilibrium. International Journal for Numerical Methods in Engineering, 36, pp.2703-2724, 1993.

    1. Babuška & R. Rodriguez: Problem of the selection of an a posteriori error indicator based on smoothing techniques. International Journal for Numerical Methods in Engineering, 36, pp.539-567, 1993.

    1. Babuška, T. Strouboulis, C. S. Upadhyay, C. S. Upadhyay, S. K. Upadhyay, S. K., S. K. Gangaraj & K. Copps: Validation of a Posterior Error Estimators by Numerical Approach. International Journal for Numerical Methods In Engineering, 37, pp.1073-1123, 1994.

    1. Babuška, T. Strouboulis, A. Mathur, A. Mathur & C. Upadhyay: Pollution-error in the h-version of the finite-element method and the local quality of a-posteriori error estimators. Finite Elements in Analysis and Design, 17, pp.273-321, 1994.

    1. Babuška, T. Strouboulis, C. S. Upadhyay & S. K. Gangaraj: A posteriori estimation and adaptive control of the pollution error in the h-version of the finite element method. International Journal for Numerical Methods in Engineering, 38, pp.4207-4235, 1995.

    1. Babuška, T. Strouboulis, S. Gangaraj & C. Upadhyay: Pollution error in the h-version of the finite element method and the local quality of the recovered derivatives. Computer Methods in Applied Mechanics and Engineering, 140, pp.1-37, 1997.

    1. Becker & R. Rannacher: An optimal control approach to shape a posteriori error estimation in finite element methods. Acta Numerica, 10, pp.1-120, 2001.

      1. Oden & S. Prudhomme: Estimation of modeling error in computational mechanics. Journal of Computational Physics, 182, pp.496-515, 2002.

  21. J.T. Oden & S. Prudhomme: Goal-oriented error estimation and adaptivity for the finite element method. Computers and Mathematics with Applications, 41, pp.735-56, 2001.

    1. Ainsworth & J.T. Oden: A posteriori error estimation in finite element analysis. Wiley-Interscience, 2000.

    1. Sauer-Budge, J. Bonet, A. Huerta & J. Peraire: Computing bounds for linear functionals of exact weak solutions to Poisson’s equation. SIAM Journal on Numerical Analysis, 42, pp.1610-1630, 2004.

    1. Prudhomme & J.T. Oden: On goal-oriented error estimation for elliptics problems: application to the control of pointwise errors. Computer Methods in Applied Mechanics and Engineering, 176, pp. 313-331, 1999.

    1. Parés, P. Díez & A. Huerta: Subdomain-based flux-free a posteriori error estimators. Computer Methods in Applied Mechanics and Engineering, 195, pp.297-323, 2006.

  26. J. Delmas: Error control strategies in the calculation of industrial structures. Implementation of error estimation in quantity of interest and mesh adaptation, doctoral thesis from the University of Picardy Jules Verne, 2008. Available for download at this address: < http://tel.archives-ouvertes.fr/tel-00311947>` http://tel.archives-ouvertes.fr/tel-00311947`_