A hybridizable discontinuous Galerkin Generalized Multiscale Finite element method for highly heterogeneous linear elasticity problems

Abstract

In this paper, we consider a multiscale hybridizable discontinuous Galerkin (HDG) for heterogeneous linear elasticity problem in a mixed formulation. Within the framework of HDG, the entire problem can be decomposed into a global problem defined in coarse interfaces and several local problems in coarse elements. Our goal here is to propose a multiscale basis space defined in the coarse interface. We will employ local snapshot spaces and local spectral decomposition following the concept of Generalized Multiscale Finite Element Methods (GMsFEM). Numerical experiments on highly heterogeneous material and nearly incompressible material are provided to verify the efficiency of the proposed method.