Unfolding homogenization in doubly periodic media and applications. Issue 13 (3rd October 2017)

• Record Type: Journal Article
• Authors: Bunoiu, Renata; Donato, Patrizia
• Is Part Of: Applicable analysis. Volume 96:Issue 13(2017)
• Page Start: 2218
• Page End: 2235
• Publication Date: 2017-10-03
• Subjects: Homogenization -- flows in porous media; 35B27 -- 76S05; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2016.1209744
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : We define a reiterated unfolding operator for a doubly periodic domain presenting two periodicity scales. Then we show how to apply it to the homogenization of both linear and nonlinear problems. The main novelty is that this method allows the use of test functions with one scale of periodicity only and it considerably simplifies the proofs of the convergence results. We illustrate this new approach on a Poisson problem with Dirichlet boundary conditions and on the flow of a power law fluid in a doubly periodic porous medium.