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

Type
Article

Authors
Mozolevski, Igor
Prudhomme, Serge

Date
2014-10-02

Abstract
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.

Citation
Mozolevski, I., & Prudhomme, S. (2015). Goal-oriented error estimation based on equilibrated-flux reconstruction for finite element approximations of elliptic problems. Computer Methods in Applied Mechanics and Engineering, 288, 127–145. doi:10.1016/j.cma.2014.09.025

Acknowledgements
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
Elsevier BV

Journal
Computer Methods in Applied Mechanics and Engineering

DOI
10.1016/j.cma.2014.09.025

Additional Links
https://linkinghub.elsevier.com/retrieve/pii/S004578251400348X

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