A Reduced Basis Approach for Variational Problems with Stochastic Parameters: Application to Heat Conduction with Variable Robin Coefficient

Abstract : In this work, a Reduced Basis (RB) approach is used to solve a large number of Boundary Value Problems (BVPs) parametrized by a stochastic input — expressed as a Karhunen-Loève expansion — in order to compute outputs that are smooth functionals of the random solution fields. The RB method proposed here for variational problems parametrized by stochastic coefficients bears many similarities to the RB approach developed previously for deterministic systems. However, the stochastic framework requires the development of new a posteriori estimates for “statistical” outputs — such as the first two moments of integrals of the random solution fields; these error bounds, in turn, permit efficient sampling of the input stochastic parameters and fast reliable computation of the outputs in particular in the many-query context.
Type de document :
Rapport
[Research Report] RR-6617, INRIA. 2008, pp.50
Liste complète des métadonnées

Littérature citée [41 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/inria-00311463
Contributeur : Sébastien Boyaval <>
Soumis le : lundi 18 août 2008 - 11:44:59
Dernière modification le : vendredi 25 mai 2018 - 12:02:03
Document(s) archivé(s) le : vendredi 5 octobre 2012 - 11:45:51

Fichier

SPDE_final.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : inria-00311463, version 1

Collections

Citation

Sébastien Boyaval, Claude Le Bris, Yvon Maday, Ngoc Cuong Nguyen, Anthony Patera. A Reduced Basis Approach for Variational Problems with Stochastic Parameters: Application to Heat Conduction with Variable Robin Coefficient. [Research Report] RR-6617, INRIA. 2008, pp.50. 〈inria-00311463〉

Partager

Métriques

Consultations de la notice

502

Téléchargements de fichiers

217