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.

在本文中，我们考虑用于混合配方中异质线性弹性问题的多尺度可杂交不连续Galerkin（HDG）。在HDG的框架内，整个问题可以分解为在粗糙接口中定义的全局问题和在粗糙元素中的几个局部问题。我们的目标是提出在粗糙界面中定义的多尺度基础空间。我们将遵循广义多尺度有限元方法（GMsFEM）的概念使用局部快照空间和局部频谱分解。通过对高度非均质材料和几乎不可压缩的材料进行数值实验，以验证该方法的有效性。