  In this paper we present new stability and optimal error analyses of
hybridized discontinuous Galerkin (HDG) methods which do not require elliptic
regularity assumptions. To obtain error estimates without elliptic regularity
assumptions, we use new inf-sup conditions based on stabilized saddle point
structures of HDG methods. We show that this approach can be applied to obtain
optimal error estimates of HDG methods for the Poisson equations, the
convection-reaction-diffusion equations, the Stokes equations, and the Oseen
equations.
