Hi David, 

Many thanks for the hint. After some research I believe I stumbled over this 
issue#7970 <https://github.com/dealii/dealii/issues/7970>? Let's see what I 
can do.

Best,
Konrad
On Tuesday, December 8, 2020 at 10:56:44 PM UTC+1 Wells, David wrote:

> Hi Konrad,
>
> This isn't a very satisfying answer but, to the best of my knowledge, 
> these Hdiv elements weren't written with general unstructured 3D meshes in 
> mind. I suspect, without looking more closely, that this is a problem on 
> our side.
>
> We document this for the FE_RaviartThomasNodal class but for 
> FE_RaviartThomas this is just a comment in the source file. Would you be 
> willing to write a patch explaining things better for the other Hdiv 
> classes?
>
> Best,
> David
> ------------------------------
> *From:* dea...@googlegroups.com <dea...@googlegroups.com> on behalf of 
> Konrad Simon <ksimo...@gmail.com>
> *Sent:* Monday, December 7, 2020 12:48 PM
> *To:* deal.II User Group <dea...@googlegroups.com>
> *Subject:* [deal.II] Div-conforming elements in 3D 
>  
> Dear Deal.ii community, 
>
> Sorry for spamming the mailing list again. I posted some of the below 
> stuff already in another post but that might have been with too many 
> unnecessary details and confusing ideas from my side.
>
> I am not sure if I stumbled over something and would like to report on 
> that. 
>
> Goal is to project a given function onto a finite element space over a 
> certain mesh. The focus here shall be on H(div)-conforming elements such as 
> Raviart-Thomas and Brezzi-Douglas-Marini Elements.
>
> I do so with several different meshes and I noticed an inconsistency in 
> the projection on meshes with, say, not so simple topology (e.g., holes and 
> voids). 
>
> Observations:
> 1. The problematic meshes do have faces with non-standard orientation. My 
> first thought was this was not carried over to the mapping of the 
> H(div)-basis but I was wrong. The mesh orientation is consistent (as far as 
> I can tell). A cube, for example, is not problematic. Please see two 
> example plots below.
>
> 2. The issue arises with both Raviart-Thomas and Brezzi-Douglas-Marini 
> Elements.
>
> 3. The issue arises in 3D only. 
>
> Any ideas what I ran into?
>
> Best,
> Konrad[image: plate_with_hole.png][image: hyper_shell.png]
>
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