A flux-based HDG method

Abstract: In this paper, we present a flux-based formulation of the hybridizable discontinuous Galerkin (HDG) method for steady-state diffusion problems and propose a new method derived by letting a stabilization parameter tend to infinity. Assuming an inf-sup condition, we prove its well-posedness and error estimates of optimal order. We show that the inf-sup condition is satisfied by some triangular elements. Numerical results are also provided to support our theoretical results.