SUPERCONVERGENCE OF HYBRIDIZABLE DISCONTINUOUS GALERKIN METHOD FOR SECOND-ORDER ELLIPTIC EQUATIONS

Abstract

A BSTRACT . We propose a projection-based analysis of a new hybridizable discontinuous Galerkin method for second order elliptic equations. The method is more advantageous than the standard HDG method in a sense that the new method has higher-order accuracy and lower computational cost, and is more flexible. Notable distinctions of our new method, when compared to the standard HDG emthod, are that our method uses L 2 − projection and suitable stabilization parameter depending on a mesh size for superconvergence. We show that the error for the solution of the equation converges with order p + 2 when we only use polynomials of degree p +1 as a finite element space without postprocessing. After establishing the theory, we carry out numerical tests to demonstrate and ensure that the proposed method is effective and accurate in practice.