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A discontinuous Galerkin multiscale method for convection-diffusion problems

Authors
  • Elfverson, Daniel
Type
Preprint
Publication Date
Sep 11, 2015
Submission Date
Sep 11, 2015
Identifiers
arXiv ID: 1509.03523
Source
arXiv
License
Yellow
External links

Abstract

We propose an discontinuous Galerkin local orthogonal decomposition multiscale method for convection-diffusion problems with rough, heterogeneous, and highly varying coefficients. The properties of the multiscale method and the discontinuous Galerkin method allows us to better cope with multiscale features as well as interior/boundary layers in the solution. In the proposed method the trail and test spaces are spanned by a corrected basis computed on localized patches of size $\mathcal{O}(H\log(H^{-1}))$, where $H$ is the mesh size. We prove convergence rates independent of the variation in the coefficients and present numerical experiments which verify the analytical findings.

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