A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems

We identify and study an LDG-hybridizable Galerkin method, which is not an LDGmethod, for second-order elliptic problems in several space dimensions with remarkable convergence properties. Unlike all other known discontinuousGalerkinmethods using polynomials of degree k ≥ 0 for both the potential as well as the flux, the order of convergence in L of both unknowns is k + 1. Moreover, both the approximate potential as well as its numerical trace superconverge in L-like norms, to suitably chosen projections of the potential, with order k+2. This allows the application of element-by-element postprocessing of the approximate solution which provides an approximation of the potential converging with order k+2 in L. The method can be thought to be in between the hybridized version of the Raviart-Thomas and that of the Brezzi-Douglas-Marini mixed methods.