[Dune] integration and assembly for polygons

[Ganesh Diwan]

Hi Dune

I recall one of my old posts on this topic:
http://lists.dune-project.org/pipermail/dune/2015-February/013459.html

In order to "build" a polygon: 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 a
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 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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