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

  • J. Tinsley Oden
  • Carlos Erik Baumann
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (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.

Keywords

Discontinuous Galerkin Method Flux Vector Interior Penalty Regular Partition Local Discontinuous Galerkin Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • J. Tinsley Oden
    • 1
  • Carlos Erik Baumann
    • 2
  1. 1.Texas Institute for Computational and Applied MathematicsUSA
  2. 2.Computational Mechanics Company, Inc.USA

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