Multiscale hybridizable discontinuous Galerkin method for elliptic problems in perforated domains

Abstract

We propose a multiscale hybridizable discontinuous Galerkin method in perforated domains. Perforations may have various shapes and sizes. Following Generalized Multiscale Finite Element method, local snapshot spaces are constructed by solving local spectral problems. Then multiscale finite element spaces for numerical traces are built on the coarse edges within the framework of hybridizable discontinuous Galerkin method. Some representative examples are presented to investigate numerical performance of the proposed method.