Titre :

Goal-oriented error estimation based on equilibrated flux and potential reconstruction for the approximation of elliptic and parabolic problems

Auteur(s) :

Creusé, Emmanuel [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
Laboratoire de Matériaux Céramiques et de Mathématiques [CERAMATHS]
Nicaise, Serge [Auteur]
Laboratoire de Matériaux Céramiques et de Mathématiques [CERAMATHS]
Tang, Zuqi [Auteur]
Laboratoire d’Électrotechnique et d’Électronique de Puissance - ULR 2697 [L2EP]

Titre de la revue :

Computers & Mathematics with Applications

Pagination :

323-338

Éditeur :

Elsevier

Date de publication :

2023

ISSN :

0898-1221

Mot(s)-clé(s) en anglais :

goal-oriented estimates
quantity of interest
elliptic and parabolic problems

Discipline(s) HAL :

Mathématiques [math]/Analyse numérique [math.NA]
Mathématiques [math]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]

Résumé en anglais : [en]

We present a unified framework for goal-oriented estimates for elliptic and parabolicproblems that combines the dual-weighted residual method with equilibrated flux and potentialreconstruction. These frameworks allow to ...
Lire la suite >We present a unified framework for goal-oriented estimates for elliptic and parabolicproblems that combines the dual-weighted residual method with equilibrated flux and potentialreconstruction. These frameworks allow to analyze simultaneously different approximationschemes for the space discretization of the primal and the dual problems such as conformingor nonconforming finite element methods, discontinuous Galerkin methods, or the finitevolume method. Our main contribution is twofold: first in a unified framework we provethe splitting of the error into a fully computable estimator $\eta$ and a remainder, second thisremainder is estimated by the product of the fully computable energy-based error estimatorsof the primal and dual problems. Some illustrative numerical examples that validate ourtheoretical results are finally presented.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL