A hybridizable direct discontinuous Galerkin method for elliptic problems

The aim of this work is to develop a hybridizable discontinuous Galerkin method for elliptic problems. In the proposed method, the numerical flux functions are constructed from the weak formulation of primal equation directly without converting the second-order equation to a first-order system. In order to guarantee the stability and convergence of the method, we derive a computable lower bound for the constant in numerical flux functions. We also establish a prior error estimation and give some theoretical analysis for the proposed method. Finally, a numerical experiment is presented to verify the theoretical results.