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Hybrid discontinuous Galerkin methods are studied for secondorder elliptic equations.Our approach is composed of generating PDEadapted local basis and solving a global matrix system arising from a flux continuity equation.Our method can be viewed as a hybridizable discontinuous Galerkin method using a Bauman-Oden type local solver.A priori and a posteriori error estimates are derived and applications to the Stokes equations and Convection-Diffusion equations are discussed.Several numerical results are presented.