• français
    • English
  • français 
    • français
    • English
  • Connexion
JavaScript is disabled for your browser. Some features of this site may not work without it.
Accueil

Afficher

Cette collectionPar Date de CréationAuteursTitresSujetsNoms de revueToute la baseCentres de recherche & CollectionsPar Date de CréationAuteursTitresSujetsNoms de revue

Mon compte

Connexion

Statistiques

Afficher les statistiques d'usage

A Reduced Basis Method for Parametrized Variational Inequalities

Thumbnail
Ouvrir
SimTechPrintsIssueNo2011-16.pdf (457.8Kb)
Date
2012
Indexation documentaire
Analyse
Subject
model reduction; reduced basis methods; variational inequalities; a posteriori error bounds
Nom de la revue
SIAM Journal on Numerical Analysis
Volume
50
Numéro
5
Date de publication
2012
Pages article
2656-2676
Nom de l'éditeur
SIAM
DOI
http://dx.doi.org/10.1137/110835372
URI
https://basepub.dauphine.fr/handle/123456789/11477
Collections
  • CEREMADE : Publications
Métadonnées
Afficher la notice complète
Auteur
Haasdonk, Bernard
Salomon, Julien
Wohlmuth, Barbara
Type
Article accepté pour publication ou publié
Résumé en anglais
Reduced basis methods are an efficient tool for significantly reducing the computational complexity of solving parametrized PDEs. Originally introduced for elliptic equations, they have been generalized during the last decade to various types of elliptic, parabolic, and hyperbolic systems. In this article, we extend the reduction technique to parametrized variational inequalities. First, we propose a reduced basis variational inequality scheme in a saddle point form and prove existence and uniqueness of the solution. We state some elementary analytical properties of the scheme such as reproduction of solutions, a priori stability with respect to the data, and Lipschitz-continuity with respect to the parameters. An offline/online decomposition guarantees an efficient assembling of the reduced scheme, which can be solved by constrained quadratic programming. Second, we provide rigorous a posteriori error bounds with a partial offline/online decomposition. The reduction scheme is applied to one-dimensional obstacle problems. The numerical results confirm the theoretical ones and demonstrate the efficiency of the reduction technique.

  • Accueil Bibliothèque
  • Site de l'Université Paris-Dauphine
  • Contact
SCD Paris Dauphine - Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16

 Cette création est mise à disposition sous un contrat Creative Commons.