A Hybridized Discontinuous Galerkin Method with Reduced Stabilization

Issei Oikawa

28 Citations (Scopus)

Abstract

In this paper, we propose a hybridized discontinuous Galerkin (HDG) method with reduced stabilization for the Poisson equation. The reduce stabilization proposed here enables us to use piecewise polynomials of degree k and k-1 for the approximations of element and inter-element unknowns, respectively, unlike the standard HDG methods. We provide the error estimates in the energy and L<sup>2</sup> norms under the chunkiness condition. In the case of k=1, it can be shown that the proposed method is closely related to the Crouzeix–Raviart nonconforming finite element method. Numerical results are presented to verify the validity of the proposed method.

Original languageEnglish
Pages (from-to)327-340
Number of pages14
JournalJournal of Scientific Computing
Volume65
Issue number1
DOIs
Publication statusPublished - 2014 Dec 2

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Keywords

  • Crouzeix–Raviart element
  • Error estimates
  • Hybridized discontinuous Galerkin methods
  • Reduced stabilization

ASJC Scopus subject areas

  • Software
  • Computational Theory and Mathematics
  • Theoretical Computer Science
  • Engineering(all)

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