  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.
