Uniform Stability and Error Analysis for Some Discontinuous Galerkin Methods

In this paper, we provide a number of new estimates on the stability and convergence both hybrid discontinuous Galerkin (HDG) weak (WG) methods. By using standard Brezzi theory mixed methods, carefully define appropriate norms for various discretization variables then establish that error hold uniformly with respect to stabilization parameters. As result, by taking limit parameters, show HDG method converges primal conforming WG converge method.