  In this paper we propose a Local Orthogonal Decomposition method (LOD) for
elliptic partial differential equations with inhomogeneous Dirichlet- and
Neumann boundary conditions. For this purpose, we present new boundary
correctors which preserve the common convergence rates of the LOD, even if the
boundary condition has a rapidly oscillating fine scale structure. We prove a
corresponding a-priori error estimate and present numerical experiments. We
also demonstrate numerically that the method is reliable with respect to thin
conductivity channels in the diffusion matrix. Accurate results are obtained
without resolving these channels by the coarse grid and without using patches
that contain the channels.
