[Dune] Dune Digest, Vol 84, Issue 22

[Carsten Gräser]

Hi Robert and Andreas,

Am 12.06.2012 14:07, schrieb 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).
can you tell me what a 2d in 3d ALUGrid does for hanging nodes:

Are they also moved according to the projection or not?
If not, does implement those piecewise smooth transformations
or will it produce holes and inconsistent element/intersection
geometries?

Best,
Carsten