Benchmark 3D: The Compact Discontinuous Galerkin 2 Scheme

Conference paper
Part of the Springer Proceedings in Mathematics book series (PROM, volume 4)

Abstract

In this paper we provide results for the 3d Benchmark on Anisotropic Diffusion Problems. We consider the Compact Discontinuous Galerkin 2 (CDG2) method first presented in [3]. In [3] a detailed stability analysis as well as a numerical investigation showing that the CDG2 method outperforms other DG methods (e.g. Bassi–Rebay 2, symmetric Interior Penalty, or the original Compact Discontinuous Galerkin Method, see [1, 3] and references therein) in terms of L2–accuracy versus computational time. Furthermore, the CDG2 method is a parameter free method in the sense that all tests have been calculated with the same set of parameters without specific test case tuning.

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References

  1. 1.
    D.N. Arnold, F. Brezzi, B. Cockburn, and L.D. Marini. Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal., 39(5):1749–1779, 2002.MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    P. Bastian, M. Blatt, A. Dedner, C. Engwer, R. Klöfkorn, R. Kornhuber, M. Ohlberger, and O. Sander. A generic grid interface for parallel and adaptive scientific computing. II: Implementation and tests in dune. Computing, 82(2-3):121–138, 2008.Google Scholar
  3. 3.
    S. Brdar, A. Dedner, and R. Klöfkorn. Compact and stable Discontinuous Galerkin methods for convection-diffusion problems. Preprint No. 2/2010-15.11-2010, Mathematisches Institut, Universität Freiburg, 2010. submitted to SIAM J. Sci. Comput.Google Scholar
  4. 4.
    A. Dedner, R. Klöfkorn, M. Nolte, and M. Ohlberger. A generic interface for parallel and adaptive discretization schemes: abstraction principles and the DUNEŰFEM; module. Computing, 90:165–196, 2010.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Section of Applied MathematicsUniversity of FreiburgFreiburgGermany

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