In this paper, we consider the constrained energy minimizing generalized multiscale finite element method (CEM-GMsFEM) with discontinuous Galerkin (DG) coupling for the linear elasticity equations in highly heterogeneous and high contrast media. We will introduce the construction of a DG version of the CEM-GMsFEM, such as auxiliary basis functions and offline basis functions. The DG version of the method offers some advantages such as flexibility in coarse grid construction and sparsity of resulting discrete systems. Moreover, to our best knowledge, this is the first time where the proof of the convergence of the CEM-GMsFEM in the DG form is given. Some numerical examples will be presented to illustrate the performance of the method.

翻译：在本文中,我们考虑了限制的能源最小化通用多尺度有限元素法(CEM-GMSFEM),在高度多样化和高对比度介质的线性弹性方程式中不连续地结合Galerkin(DG),我们将开始建造CEM-GMSFEM的DG版本,例如辅助基础功能和离线基础功能。DG方法的版本提供了一些优势,如粗糙网格构造的灵活性和由此产生的离散系统的宽度。此外,据我们所知,这是首次提供DG格式的CEM-GMSFEM趋同的证据,将提出一些数字例子来说明该方法的性能。