A Hybridized Discontinuous Galerkin Method with Reduced Stabilization

Issei Oikawa

Research output: Contribution to journalArticle

24 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

Fingerprint

Discontinuous Galerkin Method
Galerkin methods
Stabilization
Nonconforming Finite Element Method
Piecewise Polynomials
Poisson equation
Poisson's equation
Error Estimates
Polynomials
Verify
Norm
Finite element method
Unknown
Numerical Results
Approximation
Energy
Standards

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)

Cite this

A Hybridized Discontinuous Galerkin Method with Reduced Stabilization. / Oikawa, Issei.

In: Journal of Scientific Computing, Vol. 65, No. 1, 02.12.2014, p. 327-340.

Research output: Contribution to journalArticle

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