The Multiscale Discontinuous Galerkin Method for Solving a Class of Second Order Elliptic Problems with Rough Coefficients
Year: 2011
Author: W. Wang, J. Guzmán, C.-W. Shu
International Journal of Numerical Analysis and Modeling, Vol. 8 (2011), Iss. 1 : pp. 28–47
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. Theoretical 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 arbitrary order approximations. For two-dimensional problems, numerical results are presented by the high order multiscale DG method, but the error estimate is proven only for the second order method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2011-IJNAM-672
International Journal of Numerical Analysis and Modeling, Vol. 8 (2011), Iss. 1 : pp. 28–47
Published online: 2011-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: multiscale discontinuous Galerkin method rough coefficients.