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Discontinuous Galerkin Methods pp 179–196Cite as

A Conservative DGM for Convection-Diffusion and Navier-Stokes Problems

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Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 11))

Abstract

An hp—adaptive conservative Discontinuous Galerkin Method for the solution of convection-diffusion problems is reviewed. A distinctive feature of this method is the treatment of diffusion terms with a new variational formulation. This new variational formulation is not based on mixed formulations, thus having the advantage of not using flux vairables or extended stencils and/or global matrices’ bandwidth when the flux variables are statically condensed at element level.

The variational formulation for diffusion terms produces a compact, locally conservative, higher-order accurate, and stable solver. The method supports h—, p—, and hp—approximations and can be applied to any type of domain discretization, including non-matching meshes. A priori error estimates and numerical experiments indicate that the method is robust and capable of delivering high accuracy.

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Author information

Authors and Affiliations

  1. Texas Institute for Computational and Applied Mathematics, USA

    J. Tinsley Oden

  2. Computational Mechanics Company, Inc., USA

    Carlos Erik Baumann

Authors
  1. J. Tinsley Oden
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  2. Carlos Erik Baumann
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Editor information

Editors and Affiliations

  1. School of Mathematics, University of Minnesota, 206 Church Street S.E., Minneapolis, MN, 55455, USA

    Bernardo Cockburn

  2. Division of Applied Mathematics, Brown University, Providence, RI, 02912, USA

    George E. Karniadakis  & Chi-Wang Shu  & 

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© 2000 Springer-Verlag Berlin Heidelberg

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Oden, J.T., Baumann, C.E. (2000). A Conservative DGM for Convection-Diffusion and Navier-Stokes Problems. In: Cockburn, B., Karniadakis, G.E., Shu, CW. (eds) Discontinuous Galerkin Methods. Lecture Notes in Computational Science and Engineering, vol 11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59721-3_13

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  • DOI: https://doi.org/10.1007/978-3-642-59721-3_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-64098-8

  • Online ISBN: 978-3-642-59721-3

  • eBook Packages: Springer Book Archive

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