Skip to Main content Skip to Navigation
Journal articles

An analytical framework for the numerical homogenization of monotone elliptic operators and quasiconvex energies

Antoine Gloria 1
1 MICMAC - Methods and engineering of multiscale computing from atom to continuum
Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech
Abstract : A number of methods have been proposed in the recent years to perform the numerical homogenization of (possibly nonlinear) elliptic operators. These methods are usually defined at the discrete level. Most of them compute a numerical operator, close, in a sense to be made precise, to the homogenized elliptic operator for the problem. The purpose of the present work is to clarify the construction of this operator in the convex case by interpreting the method at the continuous level and to extend it to the nonconvex setting. The discretization of this new operator may be performed in several ways, recovering a variety of methods, such as the multiscale finite element method (MsFEM) or the heterogeneous multiscale method (HMM). In addition to the above, we introduce an original and general numerical corrector in the convex case.
Document type :
Journal articles
Complete list of metadatas

Cited literature [1 references]  Display  Hide  Download

https://hal.inria.fr/inria-00070230
Contributor : Rapport de Recherche Inria <>
Submitted on : Friday, May 19, 2006 - 7:36:42 PM
Last modification on : Friday, April 19, 2019 - 2:12:06 PM
Long-term archiving on: : Sunday, April 4, 2010 - 8:40:40 PM

Identifiers

Collections

Citation

Antoine Gloria. An analytical framework for the numerical homogenization of monotone elliptic operators and quasiconvex energies. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, Society for Industrial and Applied Mathematics, 2006, 5 (3), pp.996-1043. ⟨10.1137/060649112⟩. ⟨inria-00070230⟩

Share

Metrics

Record views

378

Files downloads

424