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Article Dans Une Revue Computational Methods in Applied Mathematics Année : 2021

Optimal Convergence Rates for Goal-Oriented FEM with Quadratic Goal Functional

Michael Innerberger
  • Fonction : Auteur
Dirk Praetorius
  • Fonction : Auteur

Résumé

Abstract We consider a linear elliptic PDE and a quadratic goal functional. The goal-oriented adaptive FEM algorithm (GOAFEM) solves the primal as well as a dual problem, where the goal functional is always linearized around the discrete primal solution at hand. We show that the marking strategy proposed in [M. Feischl, D. Praetorius and K. G. van der Zee, An abstract analysis of optimal goal-oriented adaptivity, SIAM J. Numer. Anal. 54 (2016), 3, 1423–1448] for a linear goal functional is also optimal for quadratic goal functionals, i.e., GOAFEM leads to linear convergence with optimal convergence rates.

Dates et versions

hal-03968586 , version 1 (01-02-2023)

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Citer

Roland Becker, Michael Innerberger, Dirk Praetorius. Optimal Convergence Rates for Goal-Oriented FEM with Quadratic Goal Functional. Computational Methods in Applied Mathematics, 2021, 21 (2), pp.267-288. ⟨10.1515/cmam-2020-0044⟩. ⟨hal-03968586⟩
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