A Spectral LOD Method for Multiscale Problems with High Contrast

Abstract: We present a multiscale finite element method for a diffusion problem with rough and high contrast coefficients. The construction of the multiscale finite element space is based on the localized orthogonal decomposition methodology and it involves solutions of local finite element eigenvalue problems. We show that the performance of the multiscale finite element method is similar to the performance of standard finite element methods for the homogeneous Dirichlet boundary value problem for the Poisson equation on smooth or convex domains.} Simple explicit error estimates are established under conditions that can be verified from the outputs of the computation.