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I have tinkered around with the implementation of hybridizable Discontinuous Galerkin (HDG) methods in DUNE-PDELab and DUNE-FEM for my PhD but since then I have not had the time to work on these codes very much. Some things were possible back then, but others such as element-wise assemblies of the facet contributions or static condensation did not fit well into the concept and required a lot of work which is most probably not compatible anymore with current versions, since it involved reimplementing certain internals. That being said, this applied to almost any framework I tried out during that time, the only exception being NGSolve (which unfortunately had some compatibility issues with Mac OS X that lead me to give up on it after a while).

Two years have passed since then and I have certain things in mind which I want to try out in the future, but I still could not find THE framework for HDG; in fact it seems like there are loads of papers published on the method and its analysis for a whole zoo of problems, but the class of HDG methods is for the most part ignored by framework developers. Am I wrong?

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The newest step 51 of the deal.ii tutorial describes the implementation and some tests of an HDG method for the convection-diffusion equation. As far as I can see there is no support for other elements than hexahedrals but the documentation of the implemented method looks excellent.

NGSolve has support for HDG which was demonstrated for convection-diffusion as well as incompressible and compressible flow problems by various authors.

It is possible to implement HDG in DUNE-PDELab (the implementation is however incompatible with current releases and has some limitations). There also exist some implementations of HDG in DUNE-FEM which are all - to my best knowledge - not publicly released.

Also I keep hearing every now and then that FEniCS has some rudimentary support for HDG but I could not find working examples.

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    $\begingroup$ FEniCS' support for HDG is somewhat limited - I haven't found a way to eliminate interior dofs in a local manner yet, and their flux basis functions (facet restrictions by their naming) do not yet support parallel assembly. $\endgroup$ – Jesse Chan Mar 19 '14 at 13:54
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    $\begingroup$ web.pdx.edu/~gjay/pub/dpglaplace.py provides an example of usage of these facet restrictions, though in a slightly different context (Demkowicz and Gopalakrishnan's DPG method). The extension to HDG should be straightforward, though. $\endgroup$ – Jesse Chan Mar 19 '14 at 13:55

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