[Dune] hanging node detection

[Carsten Gräser]

Hello Bernd,

Am 13.10.2011 16:18, schrieb Bernd Flemisch:
> Dear Dune,
> 
> can you recommend a way of detecting whether a node is hanging or not?
> It's easy if the neighboring elements are on different levels, but let's
> assume they are on the same. I can think of comparing
> intersection.geometryInInside and intersection.geometryInOutside, but
> maybe there is something nicer?

in dune-fufem we construct conforming fe spaces on grids with
hanging nodes in the following way:

For each pair of neighboring elements we evaluate the local
interpolation on one element for all local basis functions
of the other. This gives you the weights you need to construct
the conforming composite basis function. This does at least
work for Pk,Qk, and RefinedP1 local finite elements on grids
with conforming level grids.

If level grids are not conforming you can still use
this approach with P1/Q1 elements to find the hanging nodes
which are just the ones associated to all weights in (0,1).
Of coarse you must check this with some epsilon. However this
is safe for all reasonable grids.

This approach does essentially wrap all coordinate computations
in a nice way. There might be faster ways to check this, however
you cannot avoid to do some coordinate computations because this
is the only way to check if a vertex is contained in a face if
it is not a node (or copy of one) of the face.

Best,
Carsten