Can we apply FESTUNG to hdg?

[festung]

Can we apply FESTUNG to hdg?

[reuterbal]

Dear Yoczhang,
I hope my earlier reply was helpful.

At the moment there is no HDG-support implemented in FESTUNG whatsoever.
But in principle it's possible, of course, but requires some work on your side. However, I'm not an expert on HDG-methods, thus I cannot make a definite statement and the following is based on the little I know about that method:

As you already pointed out HDG requires different basis functions, which you would have to implement (functions phi() and gradPhi() are the places for that). Additionally, you will have to use other or at least additional quadrature rules (quadRule1D(), quadRule2D() are the functions where they are defined at the moment).

Regarding the integration and assembly of the matrices I'm not sure about the details of the resulting system. If you write down the discretization of your PDE(s) in some detail (like in our first paper) you will notice whether they have a structure similar to ours. In that case you could probably reuse many of our functions for the integration on reference elements and edges (integrateRefElem...() and integrateRefEdge...()) and for the assembly of the local blocks into global matrices (assembleMat...(), assembleVec...()).

I'd be interested to learn what you had to change to make FESTUNG work with HDG.

Best,
Balthasar Reuter

[yoczhang]

Dear @reuterbal
Thanks for your advice, I think I will try it after getting more familiar with the structure of FESTUNG.
Now I'm reading your second paper, your work has a great help to me.

[reuterbal]

Closing this due to inactivity.

[reuterbal]

Dear @yoczhang,
just as an information: have a look at our third paper in series, it contains an HDG discretization of linear advection.
Hope that helps,
Balthasar