Discontinuous Galerkin multiscale methods for convection dominated problems

We propose an extension of the discontinuous Galerkin multiscale method, presented in [11], to convection dominated problems with rough, heterogeneous, and highly varying coefficients. The properties of the multiscale method and the discontinuous Galerkin method allows us to better cope with multiscale features as well as boundary layers in the solution. In the proposed method the trail and test spaces are spanned by a corrected basis calculated on localized patches of size O(H log(H−1)), where H is the mesh size. We prove convergence rates independent of the variation in the coefficients and present numerical experiments which verify the analytical findings.