Goal-oriented error estimation based on equilibrated-flux reconstruction for finite element approximations of elliptic problems

Igor Mozolevski*, Serge Prudhomme

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


We propose an approach for goal-oriented error estimation in finite element approximations of second-order elliptic problems that combines the dual-weighted residual method and equilibrated-flux reconstruction methods for the primal and dual problems. The objective is to be able to consider discretization schemes for the dual solution that may be different from those used for the primal solution. It is only assumed here that the discretization methods come with a priori error estimates and an equilibrated-flux reconstruction algorithm. A high-order discontinuous Galerkin (dG) method is actually the preferred choice for the approximation of the dual solution thanks to its flexibility and straightforward construction of equilibrated fluxes. One contribution of the paper is to show how the order of the dG method for asymptotic exactness of the proposed estimator can be chosen in the cases where a conforming finite element method, a dG method, or a mixed Raviart-Thomas method is used for the solution of the primal problem. Numerical experiments are also presented to illustrate the performance and convergence of the error estimates in quantities of interest with respect to the mesh size.

Original languageEnglish (US)
Pages (from-to)127-145
Number of pages19
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - May 1 2015

Bibliographical note

Funding Information:
The first author gratefully acknowledges the partial support by CNPq , Brazil, grant number 312694/2009-1 . The second author is grateful for the support by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada , grant number RGPIN 436199-2013 . He is also a participant of the KAUST SRI center for Uncertainty Quantification in Computational Science and Engineering.

Publisher Copyright:
© 2014 Elsevier B.V.


  • Asymptotically-exact error estimates
  • Dual problem
  • Finite element method
  • Goal-oriented estimates
  • Quantity of interest

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications


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