On the homogenization of thin perforated walls of finite length

Article type: Research Article

Authors: Delourme, Bérangère^{a; *; **} | Schmidt, Kersten^{b; c} | Semin, Adrien^c

Affiliations: [a] Université Paris 13, Sorbonne Paris Cité, LAGA, UMR 7539, 93430 Villetaneuse, France | [b] Research center Matheon, 10623 Berlin, Germany | [c] Institut für Mathematik, Technische Universität Berlin, 10623 Berlin, Germany

Correspondence: [*] Corresponding author: Bérangère Delourme, Université Paris 13, Sorbonne Paris Cité, LAGA, UMR 7539, 93430 Villetaneuse, France.

Note: [**] Address: Département de Mathématiques, Institut Galilée, Université Paris 13, 99, avenue Jean-Baptiste Clément, 93430 Villetaneuse, France. Tel.: +33 (0)1 49 40 37 97; E-mail: [email protected].

Abstract: The present work deals with the resolution of the Poisson equation in a bounded domain made of a thin and periodic layer of finite length placed into a homogeneous medium. We provide and justify a high order asymptotic expansion which takes into account the boundary layer effect occurring in the vicinity of the periodic layer as well as the corner singularities appearing in the neighborhood of the extremities of the layer. Our approach combines the method of matched asymptotic expansions and the method of periodic surface homogenization.

Keywords: asymptotic analysis, periodic surface homogenization, singular asymptotic expansions

DOI: 10.3233/ASY-151350

Journal: Asymptotic Analysis, vol. 97, no. 3-4, pp. 211-264, 2016