On Discontinuous Galerkin Multiscale Methods

In this thesis a new multiscale method, the discontinuous Galerkin multiscale method, is proposed. The method uses localized fine scale computations to correct a global coarse scale equation and thereby takes the fine scale features into account. We show a priori error bounds for convection dominated convection-diffusion-reaction problems with variable coefficients. We present an posteriori error bound in the case of no convection or reaction and an adaptive algorithm which tunes the method parameters automatically. We also present extensive numerical experiments which verify our analytical findings.