  In this paper, we consider an online basis enrichment mixed generalized
multiscale method with oversampling, for solving flow problems in highly
heterogeneous porous media. This is an exten- sion of the online mixed
generalized multiscale method [6]. The multiscale online basis functions are
computed by solving a Neumann problem in an over-sampled domain, instead of a
standard neighborhood of a coarse face. We are motivated by the restricted
domain decomposition method. Extensive numerical experiments are presented to
demonstrate the performance of our methods for both steady-state flow, and
two-phase flow and transport problems.
