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 language||English (US)|
|Number of pages||19|
|Journal||Computer Methods in Applied Mechanics and Engineering|
|State||Published - May 1 2015|
Bibliographical noteFunding 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.
© 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