An extension of the Crouzeix-Raviart space to general meshes with application to quasi-incompressible linear elasticity and Stokes flow

Abstract : In this work we introduce a discrete functional space on general polygonal or polyhedral meshes which mimics two important properties of the standard Crouzeix-Raviart space, namely the continuity of mean values at interfaces and the existence of an interpolator which preserves the mean value of the gradient inside each element. The construction borrows ideas from both Cell Centered Galerkin and Hybrid Finite Volume methods. The discrete function space is defined from cell and face unknowns by introducing a suitable piecewise affine reconstruction on a (fictitious) pyramidal subdivision of the original mesh. Two applications are considered in which the discrete space plays an important role, namely (i) the design of a locking-free primal (as opposed to mixed) method for quasi-incompressible planar elasticity on general polygonal meshes; (ii) the design of an inf-sup stable method for the Stokes equations on general polygonal or polyhedral meshes. In this context, we also propose a general modification, applicable to any suitable discretization, which guarantees that the velocity approximation is unaffected by the presence of large irrotational body forces provided a Helmholtz decomposition of the right-hand side is available. The relation between the proposed methods and classical finite volume and finite element schemes on standard meshes is investigated. Finally, similar ideas are exploited to mimic key properties of the lowest-order Raviart-Thomas space on general polygonal or polyhedral meshes.
Type de document :
Article dans une revue
Mathematics of Computation, American Mathematical Society, 2015, 84 (291), pp.1-31. 〈10.1090/S0025-5718-2014-02861-5〉
Liste complète des métadonnées

Littérature citée [35 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-00753660
Contributeur : Simon Lemaire <>
Soumis le : mercredi 1 octobre 2014 - 14:55:30
Dernière modification le : mardi 24 octobre 2017 - 01:16:57
Document(s) archivé(s) le : vendredi 14 avril 2017 - 17:02:27

Fichier

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

Identifiants

Citation

Daniele Antonio Di Pietro, Simon Lemaire. An extension of the Crouzeix-Raviart space to general meshes with application to quasi-incompressible linear elasticity and Stokes flow. Mathematics of Computation, American Mathematical Society, 2015, 84 (291), pp.1-31. 〈10.1090/S0025-5718-2014-02861-5〉. 〈hal-00753660v4〉

Partager

Métriques

Consultations de la notice

427

Téléchargements de fichiers

233