A locking-free discontinuous Galerkin method for linear elasticity in locally nearly incompressible heterogeneous media

Daniele Antonio Di Pietro 1, * Serge Nicaise 2
* Auteur correspondant
1 ACSIOM
I3M - Institut de Mathématiques et de Modélisation de Montpellier
Abstract : In this work we consider the problem of numerical locking in composite materials featuring quasi-incompressible and compressible sections. More specifically, we start by extending a classical regularity estimate for the $H^1$-norm of the divergence of the displacement field to the heterogeneous case. The proof is based on a reformulation of the elasticity problem as a Stokes system with nonzero divergence constraint. This result is then used to design a locking-free discontinuous Galerkin method. The key point is to make sure that the multiplicative constant in the estimate of the convergence rate uniquely depend on this bounded quantity. Thanks to a fine tuning of the penalty term, the lower bound for the penalty parameter appearing in the method is simply expressed in terms of the space dimension. To conclude, numerical validation of the theoretical results is provided.
Type de document :
Article dans une revue
Applied Numerical Mathematics, Elsevier, 2012, 63, pp.105-116. 〈10.1016/j.apnum.2012.09.009〉
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-00685020
Contributeur : Daniele Antonio Di Pietro <>
Soumis le : mardi 3 avril 2012 - 17:09:58
Dernière modification le : mercredi 21 novembre 2018 - 14:52:10
Document(s) archivé(s) le : lundi 26 novembre 2012 - 12:45:42

Fichier

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

Identifiants

Citation

Daniele Antonio Di Pietro, Serge Nicaise. A locking-free discontinuous Galerkin method for linear elasticity in locally nearly incompressible heterogeneous media. Applied Numerical Mathematics, Elsevier, 2012, 63, pp.105-116. 〈10.1016/j.apnum.2012.09.009〉. 〈hal-00685020〉

Partager

Métriques

Consultations de la notice

314

Téléchargements de fichiers

131