[Dune] Dune Digest, Vol 84, Issue 22

[Dedner, Andreas]

Just an addition: in (almost) all grid implementations we assume that elements are smooth transformations
of a reference element e.g. the unit square. Your five vertex element could not be represented in that way, i.e.
the geometry would not be smooth. Now of course for a finite volume scheme you do not care about that
since you only need the center method and the volume both of which make sense for your 5 vertex
element - the jacobian inverse transposed is another matter....

For surface grids the new point is projected onto the surface which basically means that (as long as
the node is hanging) the elements have a certain amount of overlap). This of course only holds for hanging
nodes as soon as both neighbors are refined, the problem the point can be moved w.o. causing problems as
Carsten pointed out. Thats why for UG with red-green the problem does not arise (each element is still
a smooth mapping from a set of reference element, i.e., the unit square and triangle).

Andreas