A new goal-oriented formulation of the finite element method

Kenan Kergrene, Serge Prudhomme, Ludovic Chamoin, Marc Laforest

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


In this paper, we introduce, analyze, and numerically illustrate a method for taking into account quantities of interest during the finite element treatment of a boundary-value problem. The objective is to derive a method whose computational cost is of the same order as that of the classical approach for goal-oriented adaptivity, which involves the solution of the primal problem and of an adjoint problem used to weigh the residual and provide indicators for mesh refinement. In the current approach, we first solve the adjoint problem, then use the adjoint information as a minimization constraint for the primal problem. As a result, the constrained finite element solution is enhanced with respect to the quantities of interest, while maintaining near-optimality in energy norm. We describe the formulation in the case of a problem defined by a symmetric continuous coercive bilinear form and demonstrate the efficiency of the new approach on several numerical examples.
Original languageEnglish (US)
Pages (from-to)256-276
Number of pages21
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - Dec 2017
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2021-04-06
Acknowledged KAUST grant number(s): CRG3, OCRF-2014-CRG
Acknowledgements: SP is grateful for the support by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada. He also acknowledges the support by KAUST under Award Number OCRF-2014-CRG3-2281. Moreover, the authors gratefully acknowledge Jonathan Vacher for fruitful discussions on the subject.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

ASJC Scopus subject areas

  • General Physics and Astronomy
  • Mechanics of Materials
  • Mechanical Engineering
  • Computational Mechanics
  • Computer Science Applications


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