INTERIOR ERROR ESTIMATE FOR PERIODIC HOMOGENIZATION

In a previous paper about homogenization of the classical problem of diffusion in a bounded domain with sufficiently smooth boundary, we proved that the global error is of order ε1/2. Now, for an open set Ω with sufficiently smooth boundary [Formula: see text] and homogeneous Dirichlet or Neumann limit conditions, we show that in any open set strongly included in Ω the error is of order ε. If the open set Ω ⊂ ℝn is of polygonal (n = 2) or polyhedral (n = 3) boundary, we also give the global and interior error estimates.