MsFEM à la Crouzeix-Raviart for Highly Oscillatory Elliptic Problems

Claude Le Bris (1, 2) , Frédéric Legoll (2, 3) , Alexei Lozinski (4, 5)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
2 MICMAC - Methods and engineering of multiscale computing from atom to continuum
3 multi-échelle - Modélisation et expérimentation multi-échelle pour les solides hétérogènes
4 IMT - Institut de Mathématiques de Toulouse UMR5219
5 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

We introduce and analyze a multiscale finite element type method (MsFEM) in the vein of the classical Crouzeix-Raviart finite element method that is specifically adapted for highly oscillatory elliptic problems. We illustrate numerically the efficiency of the approach and compare it with several variants of MsFEM.

Mots clés: Homogenization; Finite elements; Galerkin methods; Highly oscillatory PDE

Domaines: Analyse numérique [math.NA]

Claude Le Bris, Frédéric Legoll, Alexei Lozinski. MsFEM à la Crouzeix-Raviart for Highly Oscillatory Elliptic Problems. Chinese Annals of Mathematics - Series B, 2013, 34 (1), pp.113-138. ⟨10.1007/s11401-012-0755-7⟩. ⟨hal-00789102⟩