Corrector estimates for a class of imperfect transmission problems

Article type: Research Article

Authors: Reichelt, Sina

Affiliations: Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS), Mohrenstraße 39, 10117 Berlin, Germany. E-mail: reichelt@wias-berlin.de

Abstract: Based on previous homogenization results for imperfect transmission problems in two-component domains with periodic microstructure, we derive quantitative estimates for the difference between the microscopic and macroscopic solution. This difference is of order ερ, where ε>0 describes the periodicity of the microstructure and ρ∈(0,12] depends on the transmission condition at the interface between the two components. The corrector estimates are proved without assuming additional regularity for the local correctors using the periodic unfolding method.

Keywords: Homogenization, corrector results, error estimates, periodic unfolding, two-component domain, periodic interface, imperfect transmission

DOI: 10.3233/ASY-171432

Journal: Asymptotic Analysis, vol. 105, no. 1-2, pp. 3-26, 2017