Two-scale homogenization of the Poisson equation with friction boundary condition in a perforated domain

Article type: Research Article

Authors: Baffico, L.

Affiliations: Laboratoire de Mathématiques Nicolas Oresme, CNRS UMR 6139, Université de Caen Basse-Normandie, Caen, France. Tel.: +33 231567440; Fax: +33 231567320; E-mail: [email protected]

Abstract: We study the homogenization of the Poisson equation in a periodically perforated domain, of period ε>0, with a friction type boundary condition on the holes’ boundary. This non-linear condition allows the solution to be non-zero on the periodic boundary if some conditions are satisfied. Using two-scale convergence results we prove that the solution of the mixed variational formulation converges, as ε goes to 0, to the solution of a two-scale mixed problem. We also prove that this homogenized problem is well-posed. A numerical test is done, using the Finite Element Method and a quadratic programming algorithm, in order to compare the heterogeneous and homogenized solutions.

Keywords: homogenization, variational inequalities, mixed formulation

DOI: 10.3233/ASY-151346

Journal: Asymptotic Analysis, vol. 96, no. 3-4, pp. 331-349, 2016