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In this paper we consider the numerical upscaling of the Brinkman equation inthe presence of high-contrast permeability fields. We develop and analyze arobust and efficient Generalized Multiscale Finite Element Method (GMsFEM) forthe Brinkman model. In the fine grid, we use mixed finite element method withthe velocity and pressure being continuous piecewise quadratic and piecewiseconstant finite element spaces, respectively. Using the GMsFEM framework weconstruct suitable coarse-scale spaces for the velocity and pressure that yielda robust mixed GMsFEM. We develop a novel approach to construct a coarseapproximation for the velocity snapshot space and a robust small offline spacefor the velocity space. The stability of the mixed GMsFEM and a priori errorestimates are derived. A variety of two-dimensional numerical examples arepresented to illustrate the effectiveness of the algorithm.

A Generalized Multiscale Finite Element Method for the Brinkman Equation