Thank you, Daniel. That confirms my intuition about that. The push forward 
from the ref cell to physical cells is, I found after thinking about it 
again, for RaviartThomas, BDM, Nedelec elements etc not the same as a Piola 
transform (which eliminates scaling but not rotation). My code works now 
without having to rescale.

Thanks again :-)

Konrad

On Monday, March 18, 2019 at 11:17:40 AM UTC+1, Daniel Arndt wrote:
>
>  Konrad,
>  
>  I implemented a class derived from the Function<dim> class that evaluates 
> a scalar or vector shape function at a given (set of) point(s) in a 
> physical cell. If I check the output graphically I see that the vector 
> shape    functions on the physical cell, for example for lowest order 
> Raviart-Thomas elements has a magnitude that scales with the inverse edge 
> length. But on any physical cell the magnitude should be one I believe.
>  
>   For the Raviart-Thomas the degrees of freedom for the lowest order 
> element should be the face integrals. Hence, I would expect them to scale 
> with the (inverse of the) size of the face.
>  
>  
> I assume that has something to do with the mapping used by the FEValues 
> class to map to the physical cell, right? Does the FEValues class initiated 
> with any vector element use the Piola transform? If not how can I influence 
> this?
>  
>  Have a look at 
> https://www.dealii.org/current/doxygen/deal.II/group__mapping.html. The 
> transformation type used in Mapping::transform() is normally set by the 
> given FiniteElement class.
>  
>  Best,
>  Daniel
>

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