Error estimates in periodic homogenization with a non-homogeneous Dirichlet condition

TL;DR

This paper provides error estimates for periodic homogenization problems with non-homogeneous Dirichlet boundary conditions using the unfolding method, advancing understanding of boundary data effects.

Contribution

It introduces error estimates for homogenization with boundary data in $H^{1/2}(oundary\,Omega)$, utilizing the unfolding method to handle non-homogeneous Dirichlet conditions.

Findings

Error estimates derived for boundary data in $H^{1/2}(oundary\,Omega)$

Application of unfolding method to non-homogeneous boundary conditions

Enhanced understanding of boundary effects in periodic homogenization

Abstract

In this paper we investigate the homogenization problem with a non-homogeneous Dirichlet condition. Our aim is to give error estimates with boundary data in $H^{1/2}(\partial\Omega)$. The tools used are those of the unfolding method in periodic homogenization.