Mixed multiscale finite element methods using limited global information

In this paper, we present a mixed multiscale finite element method using limited global information. We consider a general case where multiple global information is given such that the solution depends smoothly on these global fields. The global fields typically contain smallscale (local or global) information required for achieving a convergence with respect to the coarse mesh size. We present a rigorous analysis and show that the proposed mixed multiscale finite element methods converge. Some preliminary numerical results are shown. We study a parameter dependent permeability field (a simplified case for general stochastic permeability fields). As for spatial heterogeneities, channelized permeability fields with strong nonlocal effects are considered. Using a few global fields corresponding to realizations of permeability fields, we show that one can achieve high accuracy in numerical simulations.