The DG methods are ideally suited for numerically solving hyperbolic problems.
However this is not the case for diffusion problems,even though they are ideally suited for
hp-adaptivity. Indeed, when compared with the classical continuous Galerkin methods
on the same mesh, they have many more global degrees of freedom and they are not easy
to implement. When compared with the mixed methods, they do not provide optimally
convergent approximations to the flux and do not display superconvergence properties
of the scalar variable. As a response to these disadvantages, the HDG methods were
introduced in . Therein, it was shown that HDG methods can be implemented as
efficiently as the mixed methods. Later in  it was proven that the HDG methods
do share with mixed methods their superior convergence properties while retaining the
advantages typical of the DG methods. Inspired by these results, in this Thesis we are trying to explore HDG methods in a wider circumstance.