Goal-oriented adaptive finite element methods with optimal computational complexity - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Numerische Mathematik Année : 2023

Goal-oriented adaptive finite element methods with optimal computational complexity

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

Résumé

Abstract We consider a linear symmetric and elliptic PDE and a linear goal functional. We design and analyze a goal-oriented adaptive finite element method, which steers the adaptive mesh-refinement as well as the approximate solution of the arising linear systems by means of a contractive iterative solver like the optimally preconditioned conjugate gradient method or geometric multigrid. We prove linear convergence of the proposed adaptive algorithm with optimal algebraic rates. Unlike prior work, we do not only consider rates with respect to the number of degrees of freedom but even prove optimal complexity, i.e., optimal convergence rates with respect to the total computational cost.

Dates et versions

hal-03968557 , version 1 (01-02-2023)

Identifiants

Citer

Roland Becker, Gregor Gantner, Michael Innerberger, Dirk Praetorius. Goal-oriented adaptive finite element methods with optimal computational complexity. Numerische Mathematik, 2023, 153 (1), pp.111-140. ⟨10.1007/s00211-022-01334-8⟩. ⟨hal-03968557⟩
13 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More