A generalized finite element method for problems with sign-changing coefficients

Problems with sign-changing coefficients occur, for instance, in the study of transmission problems metamaterials. In this work, we present and analyze a generalized finite element method spirit localized orthogonal decomposition, that is especially efficient when negative positive materials exhibit multiscale features. We derive optimal linear convergence energy norm independently potentially low regularity exact solution. Numerical experiments illustrate theoretical rates show applicability large class diffusion problems.