[Dune] hanging node detection

[Bernd Flemisch]

Hey Carsten,

that does not sound so bad, I will try that.

Thank you for your fast answer. Kind regards
Bernd

On Thu, 13 Oct 2011 17:05:22 +0200
  Carsten Gräser <graeser at math.fu-berlin.de> wrote:
> 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

___________________________________________________________

Bernd Flemisch                     phone: +49 711 685 
69162
IWS, Universitaet Stuttgart          fax: +49 711 685 
67020
Pfaffenwaldring 61        email: 
bernd at iws.uni-stuttgart.de
D-70569 Stuttgart        url: 
www.hydrosys.uni-stuttgart.de
___________________________________________________________