  In this paper we use the GeneralizedMultiscale Finite ElementMethod (GMsFEM)
framework, introduced in [20], in order to solve nonlinear elliptic equations
with high-contrast coefficients. The proposed solution method involves
linearizing the equation so that coarse-grid quantities of previous solution
iterates can be regarded as auxiliary parameters within the problem
formulation. With this convention, we systematically construct respective
coarse solution spaces that lend themselves to either continuous Galerkin (CG)
or discontinuous Galerkin (DG) global formulations. Here, we use Symmetric
Interior Penalty Discontinuous Galerkin approach. Both methods yield a
predictable error decline that depends on the respective coarse space
dimension, and we illustrate the effectiveness of the CG and DG formulations by
offering a variety of numerical examples.
