  In this paper, we develop an adaptive Generalized Multiscale Discontinuous
Galerkin Method (GMs-DGM) for a class of high-contrast flow problems, and
derive a-priori and a-posteriori error estimates for the method. Based on the
a-posteriori error estimator, we develop an adaptive enrichment algorithm for
our GMsDGM and prove its convergence. The adaptive enrichment algorithm gives
an automatic way to enrich the approximation space in regions where the
solution requires more basis functions, which are shown to perform well
compared with a uniform enrichment. We also discuss an approach that adaptively
selects multiscale basis functions by correlating the residual to multiscale
basis functions (cf. [4]). The proposed error indicators are L2-based and can
be inexpensively computed which makes our approach efficient. Numerical results
are presented that demonstrate the robustness of the proposed error indicators.
