A Hybridized Discontinuous Galerkin Method with Reduced Stabilization
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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.
KeywordsHybridized discontinuous Galerkin methods Error estimates Reduced stabilization Crouzeix–Raviart element
Mathematics Subject Classification65N30
This work was supported by JSPS KAKENHI Grant Number 24224004, 26800089.
- 14.Lehrenfeld, C.: Hybrid Discontinuous Galerkin Methods for Solving Incompressible Flow Problems. PhD Thesis, RWTH Aachen University (2010)Google Scholar
- 15.Lyness, J.N., Cools, R.: A Survey of Numerical Cubature Over Triangles. Proc. Symp. Appl. Math. 48, 127–150 (1994)Google Scholar