Multiscale Discontinuous Galerkin Methods for Elliptic Problems with Multiple Scales

Navier-Stokes/darcy coupling: modeling, analysis, and numerical approximation

“…While methods based on homogenization theory are usually limited by restrictive assumptions on the media such as scale separation and periodicity, besides being expensive to use for solving problems with many separate scales, the number of scales is irrelevant for the multiscale finite element method. It is worth to note that multiscale finite element methods have also been developed in their adaptive [2], discontinuous [3] and mixed [5] version.…”

Discontinuous Galerkin finite element heterogeneous multiscale method for elliptic problems with multiple scales

“…The formulation of this latter method (based on the local discontinuous Galerkin method) differs from the method proposed in the present paper. Another DG-FEM for multiscale elliptic problems has been proposed in [1]. This method is constructed in the framework of the multiscale finite element (MsFEM) framework of [35].…”

A multiscale reduced-basis method for parametrized elliptic partial differential equations with multiple scales

“…Several multiscale methods such as the multiscale FE method [15,16], multiscale finite volume method [17], mixed multiscale FE method [8], and multiscale discontinuous Galerkin method [1] have been proposed for multiscale modeling and analysis. In these methods, one does not alter the differential coefficients, but instead one constructs coarse-scale approximation spaces that reflect subgrid structures in a way consistent with the local property of the differential operator.…”