  Convergence and compactness properties of approximate solutions to elliptic
partial differential computed with the hybridized discontinuous Galerkin (HDG)
are established. While it is known that solutions computed using the HDG scheme
converge at optimal rates to smooth solutions, this does not establish the
stability of the method or convergence to solutions with minimal regularity.
The compactness and convergence results show that the HDG scheme can be
utilized for the solution of nonlinear problems and linear problems with
non-smooth coefficients on domains with reentrant corners.
