Goal-oriented adaptivity of mixed GMsFEM for flows in heterogeneous media

We present an adaptive goal-oriented framework with the mixed Generalized Multiscale Finite Element Method (GMsFEM) to numerically solve the flow problem in heterogeneous media. In this paper, three different error indicators are considered: two, goal-oriented, and one a standard adaptive method for the global error. Each is used to approximate a number of quantities of interest given by interior edge fluxes in a high-contrast field. Following the setting of mixed GMsFEM, on each coarse neighborhood of the computational domain, the local error indicator introduced here is computed by the product of the residual norms of the primal and dual variational equations over coarse neighborhoods. Numerical results demonstrate the efficiency of this goal-oriented method in comparison to a multiscale implementation of the dual weighted residual method, and a standard adaptive method.