Homogenization and two-scale convergence - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue SIAM Journal on Mathematical Analysis Année : 1992

Homogenization and two-scale convergence

Résumé

Following an idea of G. Nguetseng, we define a notion of "two-scale" convergence, which is aimed to a better description of sequences of oscillating functions. Bounded sequences in $L^2(\Omega)$ are proved to be relatively compact with respect to this new type of convergence. We also establish a corrector-type theorem (i.e. which permits, in some cases, to replace a sequence by its "two-scale" limit, up to a strongly convergent remainder in $L^2(\Omega)$). These results are especially useful for the homogenization of partial differential equations with periodically oscillating coefficients. In particular, we propose a new method for proving the convergence of homogenization processes, which is an alternative to the so-called energy method of L. Tartar. The power and simplicity of the two-scale convergence method is demonstrated on several examples, including the homogenization of both linear and non-linear second-order elliptic equations.
Fichier principal
Vignette du fichier
two-scale.pdf (4.12 Mo) Télécharger le fichier
Origine : Fichiers éditeurs autorisés sur une archive ouverte
Loading...

Dates et versions

hal-01111805 , version 1 (04-02-2020)

Identifiants

  • HAL Id : hal-01111805 , version 1

Citer

Grégoire Allaire. Homogenization and two-scale convergence. SIAM Journal on Mathematical Analysis, 1992, 23 (6), pp.1482-1518. ⟨hal-01111805⟩

Collections

CEA INSMI TDS-MACS
452 Consultations
463 Téléchargements

Partager

Gmail Facebook X LinkedIn More