Edge Multiscale Finite Element Methods

Abstract

The objective of this paper is to review recent developments in Edge Multiscale Finite Element Methods (EMsFEM) for partial differential equations with heterogeneous coefficients or highly oscillatory solutions. Using elliptic equations with heterogeneous coefficients as an illustrative example, we present the key ideas of the method. We also analyze the approach while accounting for the discrete error in the multiscale basis functions. Extensive numerical tests are provided to validate the performance of the method.