Identifier: 2009-38
Author(s): W. Wang, J. Guzman, and C.-W. Shu
Title: The multiscale discontinuous Galerkin method for solving a class of second order elliptic problems with rough coefficients
Page count: 21 pp.
Date: 2009-10-29
Abstract:
We develop a multiscale discontinuous Galerkin (DG) method for solving a class of second order elliptic problems with rough coefficients. The main ingredient of this method is to use a non-polynomial multiscale approximation space in the DG method to capture the multiscale solutions using coarse meshes without resolving the fine scale structure of the solution. The- oretical proofs and numerical examples are presented in both one and two dimensions. For one-dimensional problems, optimal error estimates and numerical examples are shown for arbi- trary order approximations. For two-dimensional problems, numerical results are presented by high order multiscale DG method, but the error estimate is proven only for the second order method.
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