Homogenization and boundary layers

By Davdi Gerard-Varet, Nader Masmoudi. 2012

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This paper deals with the homogenization of elliptic systems with Dirichlet boundary condition, when the coefficients of both the system and the boundary data are e-periodic. We show that, as e → 0, the solutions converge in L2 with a power rate in e, and identify the homogenized limit system. Due to a boundary layer phenomenon, this homogenized system depends in a non trivial way on the boundary. Our analysis answers a longstanding open problem, raised for instance in [7]. It extends substantially previous results obtained for polygonal domains with sides of rational slopes as well as our previous paper [12] where the case of irrational slopes was considered.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/377c301c9114fd08c9e54710f475538e951a2db4