[dune-fem] integration and assembly for polygons

[Ganesh Diwan]

Dear Dune-Fem developers,

I recall one of my old posts on this topic:
http://lists.dune-project.org/pipermail/dune/2015-February/013459.html
which I had posted on main Dune mailing list. I am trying to build my
Dune-Vem module under Dune-Fem by trying to use as much functions from
Dune-fem as possible.

In order to "build" a polygon for my method: I first create a mesh the
usual way (either Gmsh or in Dune itself) and then partition it using
ParMETIS to agglomerate the finite elements. One such agglomerated unit is
one of my polygons and so on.

Now, I am trying to understand if it will be possible to treat these
polygons (which are basically agglomerated finite elements) as finite
elements in their own right in Dune? I can compute a given function f at
the quadrature points inside the polygons and do int_Omega f,  but
obviously I need more. For eg, if an agglomeration can be treated as one
finite element, how do I evaluate the basis function phi_i, its derivatives
and then do a subsequent assembly for them? To be precise, the methods
which are already in place in dune-fem to do exactly this, can I use them
to operate on my polygons? For eg. when reusing the dune-fem code, I would
like to use methods such as localFunction.evaluate, rhsLocal.axpy and
rhs.communicate but I do not understand how to and what to change in order
to achieve this.

Many thanks for your help,
Ganesh
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