Nonconforming generalized multiscale finite element methods

A framework is introduced for nonconforming multiscale approach based on GMsFEM (Generalized Multiscale Finite Element Method). Snapshot spaces are constructed for each macro-scale block. The snapshot spaces can be based on either conforming or nonconforming elements. With suitable dimension reduction, offline spaces are constructed. Moment function spaces are then introduced to impose continuity among the local offline spaces, which results in nonconforming GMsFE spaces. Oversampling and randomized boundary condition strategies are considered. Steps for the nonconforming GMsFEM are given explicitly. Error estimates are derived. Numerical results are presented to support the efficiency of the proposed approach. (C) 2016 Elsevier B.V. All rights reserved.