A Hybridized Discontinuous Galerkin Method with Reduced Stabilization

Issei Oikawa

doi:10.1007/s10915-014-9962-6

A Hybridized Discontinuous Galerkin Method with Reduced Stabilization

Issei Oikawa^*

^*Corresponding author for this work

Waseda Research Institute for Science and Engineering

Research output: Contribution to journal › Article › peer-review

42 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 language	English
Pages (from-to)	327-340
Number of pages	14
Journal	Journal of Scientific Computing
Volume	65
Issue number	1
DOIs	https://doi.org/10.1007/s10915-014-9962-6
Publication status	Published - 2014 Dec 2

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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10.1007/s10915-014-9962-6

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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 L2 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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AB - 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 L2 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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A Hybridized Discontinuous Galerkin Method with Reduced Stabilization

Abstract

Keywords

ASJC Scopus subject areas

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