Localized Orthogonal Decomposition Method with $H^1$ Interpolation for Multiscale Elliptic Problem

This paper employs a localized orthogonal decomposition (LOD) method with $H^1$ interpolation for solving the multiscale elliptic problem. This method does not need any assumptions on scale separation. We give a priori error estimate for the proposed method. The theoretical results are conformed by various numerical experiments.