TY - JOUR
T1 - A Hybridized Discontinuous Galerkin Method with Reduced Stabilization
AU - Oikawa, Issei
PY - 2014/12/2
Y1 - 2014/12/2
N2 - 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.
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.
KW - Crouzeix–Raviart element
KW - Error estimates
KW - Hybridized discontinuous Galerkin methods
KW - Reduced stabilization
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U2 - 10.1007/s10915-014-9962-6
DO - 10.1007/s10915-014-9962-6
M3 - Article
AN - SCOPUS:84941313616
SN - 0885-7474
VL - 65
SP - 327
EP - 340
JO - Journal of Scientific Computing
JF - Journal of Scientific Computing
IS - 1
ER -