The Multiscale Discontinuous Galerkin Method for Solving a Class of Second Order Elliptic Problems with Rough Coefficients

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.

Author Details

W. Wang

J. Guzmán

C.-W. Shu