A finite element method for elliptic problems with rapidly oscillating coefficients (Q878211)

The authors solve second-order elliptic problems with rapidly oscillating coefficients. Under the assumption that the oscillating coefficients are periodic they present a finite element method whose key is to combine a numerical approximation of the 1-order approximate solution of those equations and a numerical approximation of the classical boundary corrector of those equations from different meshes exploiting the need for different levels of resolution. The paper is carefully written and the numerical support is adequate. However, it took the reviewer a few moments to realize that in the numerical examples the functions \(a_{ij}\) are extended beyond \([0,1] \times [0,1]\) by periodicity. An example with intrinsically periodic functions would in a sense be more natural.