A hybridized discontinuous Galerkin method with reduced stabilization
This work offers an incremental improvement in numerical methods for solving the Poisson equation, potentially reducing computational cost while maintaining accuracy.
The paper proposes a hybridized discontinuous Galerkin method with reduced stabilization for the Poisson equation, enabling the use of piecewise polynomials of degree k and k-1 for element and inter-element unknowns, respectively. Error estimates in energy and L2 norms are provided, and numerical results verify the method's validity.
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.