  We propose an discontinuous Galerkin local orthogonal decomposition
multiscale method for convection-diffusion 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 interior/boundary layers in the solution. In the proposed
method the trail and test spaces are spanned by a corrected basis computed on
localized patches of size $\mathcal{O}(H\log(H^{-1}))$, 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.
