Subdomain-based flux-free a posteriori error estimators

Author (s): Núria Parés, Pedro Díez and Antonio Huerta
Journal: Computer Methods in Applied Mechanics and Engineering

Volume: 195, Issues 4-6
Pages: 297 – 323
Date: 2006

A new residual type flux-free error estimator is presented. It estimates upper and lower bounds of the error in energy norm. The proposed approach precludes the main drawbacks of standard residual type estimators, circumvents the need of flux-equilibration and results in a simple implementation that uses standard resources available in .nite element codes. This is specially interesting for 3D applications where the implementation of this technique is as simple as in 2D. Recall that on the contrary, the complexity of the flux-equilibration techniques increases drastically in the 3D case. The bounds for the energy norm of the error are used to produce upper and lower bounds of linear functional outputs, representing
quantities of engineering interest. The presented estimators demonstrate their efficiency in numerical tests producing sharp estimates both for the energy and the quantities of interest.



  Author   = {Par{{\'e}}s, N{{\'u}}ria and D{\'{\i}}ez, Pedro and Huerta, Antonio},
  Title    = {Subdomain-based flux-free a posteriori error estimators},
  Fjournal = {Computer Methods in Applied Mechanics and Engineering},
  Journal  = {Comput. Methods Appl. Mech. Engrg.},
  Volume   = {195},
  Number   = {4-6},
  Pages    = {297--323},
  Year     = {2006},
  Doi      = {10.1016/j.cma.2004.06.047},
  Url      = {http://www.ams.org/mathscinet-getitem?mr=2186139}}