| 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. |
