Exponential Convergence of hp-DGFEM for Elliptic Problems in Polyhedral Domains

  • Dominik Schötzau
  • Christoph Schwab
  • Thomas Wihler
  • Marcel Wirz
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 95)

Abstract

We review the recent results of D. Schötzau et al. (hp-dGFEM for elliptic problems in polyhedra. I: Stability and quasioptimality on geometric meshes. Technical report 2009-28, Seminar for applied mathematics, ETH Zürich, 2009. To appear in SIAM J Numer Anal, 2013; hp-dGFEM for elliptic problems in polyhedra. II: Exponential convergence. Technical report 2009-29, Seminar for applied mathematics, ETH Zürich, 2009. To appear in SIAM J Numer Anal, 2013), and establish the exponential convergence of hp-version discontinuous Galerkin finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems with homogeneous Dirichlet boundary conditions and constant coefficients in three-dimsional and axiparallel polyhedra. The exponential rates are confirmed in a series of numerical tests.

Notes

Acknowledgements

This work was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC), the European Research Council AdG grant STAHDPDE 247277, and the Swiss National Science Foundation (SNF, Grant 200020 144442/1).

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Dominik Schötzau
    • 1
  • Christoph Schwab
    • 2
  • Thomas Wihler
    • 3
  • Marcel Wirz
    • 3
  1. 1.Department of MathematicsUniversity of British ColumbiaVancouverCanada
  2. 2.Seminar for Applied Mathematics, ETHZürichSwitzerland
  3. 3.Mathematisches InstitutUniversität BernBernSwitzerland

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