Abstract

We introduce a new class of discontinuous Galerkin (DG) methods for solving elliptic problems with multiple scales arising from e.g., composite materials and flows in porous media. The proposed methods may be seen as a generalization of the multiscale finite element (FE) methods. In fact, the proposed DG methods are derived by combining the approximation spaces for the multiscale FE methods and relaxing the continuity constraints at the inter-element interfaces. We demonstrate the performance of the proposed DG methods through numerical comparisons with the multiscale FE methods for elliptic problems in two dimensions.

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