The periodic unfolding for a Fredholm alternative in perforated domains

D Cioranescu , A Damlamian (1) , G Griso (2)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 LJLL - Laboratoire Jacques-Louis Lions

We consider the homogenization of a pure Neumann boundary value problem in perforated domains. Contrary to the usual case, several obstructions occur in this case. We present an approximation of the domains for which the problem is well-posed and homogenization can be proved. The main tool is the unfolding method together with geometrical results used to establish uniform bounds.

Domaines: Analyse numérique [math.NA]

D Cioranescu, A Damlamian, G Griso. The periodic unfolding for a Fredholm alternative in perforated domains. IMA Journal of Applied Mathematics, 2012, 77, pp.837 - 854. ⟨10.1093/imamat/hxs051⟩. ⟨hal-01450046⟩