A new goal-oriented formulation of the finite element method

Kenan Kergrene, Serge Prudhomme, Ludovic Chamoin, Marc Laforest

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

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
Volume327
DOIs
StatePublished - Dec 2017
Externally publishedYes

ASJC Scopus subject areas

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

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