A Hybridized Discontinuous Galerkin Method with Reduced Stabilization

Journal of Scientific Computing volume 65, pages327–340(2015)Cite this 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.

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Acknowledgments

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

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  1. Faculty of Science and Engineering, Waseda University, Tokyo, Japan

    Issei Oikawa

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  1. Issei Oikawa
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Correspondence to Issei Oikawa.

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Oikawa, I. A Hybridized Discontinuous Galerkin Method with Reduced Stabilization. J Sci Comput 65, 327–340 (2015). https://doi.org/10.1007/s10915-014-9962-6

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Keywords

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

Mathematics Subject Classification

  • 65N30