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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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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DOI: https://doi.org/10.1007/s10915-014-9962-6
Keywords
- Hybridized discontinuous Galerkin methods
- Error estimates
- Reduced stabilization
- Crouzeix–Raviart element