The heterogeneous multiscale finite element method for elliptic homogenization problems in perforated domains

Henning P, Ohlberger M

Abstract

In this contribution we analyze a generalization of the heterogeneous multiscale finite element method for elliptic homogenization problems in perforated domains. The method was originally introduced by E and Engquist (Commun Math Sci 1(1):87–132, 2003) for homogenization problems in fixed domains. It is based on a standard finite element approach on the macroscale, where the stiffness matrix is computed by solving local cell problems on the microscale. A-posteriori error estimates are derived in L²(Ω) by reformulating the problem into a discrete two-scale formulation and using duality methods afterwards. Numerical experiments are given in order to numerically evaluate the efficiency of the error estimate.