PERIODIC UNFOLDING FOR ANISOTROPICALLY BOUNDED SEQUENCES

Georges Griso (1) , Riccardo Falconi (2) , Julia Orlik (2)

1 LJLL - Laboratoire Jacques-Louis Lions
2 Fraunhofer ITWM - Fraunhofer Institute of Industrial Mathematics

This paper is focused on the asymptotic behavior of sequences of functions, whose partial derivatives estimates in one or more directions are highly contrasted with respect to the periodic parameter ε. In particular, a direct application for the homogenization of a homogeneous Dirichlet problem defined on an anisotropic structure is presented. In general, the obtained results can be applied to thin structures where the behavior is different according to the observed direction.

Mots clés: Periodic unfolding method; homogenization; anisotropic Sobolev spaces; Dirichlet problem

Domaines: Analyse numérique [math.NA]; Mathématiques [math]

Georges Griso, Riccardo Falconi, Julia Orlik. PERIODIC UNFOLDING FOR ANISOTROPICALLY BOUNDED SEQUENCES. 2020. ⟨hal-03532607⟩