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Volume 8, Issue 1
The Multiscale Discontinuous Galerkin Method for Solving a Class of Second Order Elliptic Problems with Rough Coefficients

W. Wang, J. Guzmán & C.-W. Shu

Int. J. Numer. Anal. Mod., 8 (2011), pp. 28-47.

Published online: 2011-08

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  • 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.

  • Keywords

multiscale discontinuous Galerkin method, rough coefficients.

  • AMS Subject Headings

65N30

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{IJNAM-8-28, author = {Wang , W.Guzmán , J. and Shu , C.-W.}, title = {The Multiscale Discontinuous Galerkin Method for Solving a Class of Second Order Elliptic Problems with Rough Coefficients}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2011}, volume = {8}, number = {1}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/672.html} }
TY - JOUR T1 - The Multiscale Discontinuous Galerkin Method for Solving a Class of Second Order Elliptic Problems with Rough Coefficients AU - Wang , W. AU - Guzmán , J. AU - Shu , C.-W. JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 28 EP - 47 PY - 2011 DA - 2011/08 SN - 8 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/672.html KW - multiscale discontinuous Galerkin method, rough coefficients. AB -

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.

Wang , W.Guzmán , J. and Shu , C.-W.. (2011). The Multiscale Discontinuous Galerkin Method for Solving a Class of Second Order Elliptic Problems with Rough Coefficients. International Journal of Numerical Analysis and Modeling. 8 (1). 28-47. doi:
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