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Journal of Scientific Computing

, Volume 65, Issue 1, pp 327–340 | Cite as

A Hybridized Discontinuous Galerkin Method with Reduced Stabilization

  • Issei OikawaEmail author
Article

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 \(L^2\) 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.

Keywords

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

Mathematics Subject Classification

65N30 

Notes

Acknowledgments

This work was supported by JSPS KAKENHI Grant Number 24224004, 26800089.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Faculty of Science and EngineeringWaseda UniversityTokyoJapan

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