Hi Wolfgang,

your explanation makes indeed more sense in the context of piecewise 
polynomials :)

The problem here is that the solution is not continuous across the face of 
a FE_Q and a FE_Nothing element. If a FE_Nothing is turned into a FE_Q 
element, the solution is suddenly expected to be continuous, and we have no 
rule in deal.II yet how to continue in the situation. In my opinion, we 
should throw an assertion in this case.

I have a patch for the p::d case in mind what will warn users about this: 
we should reinit the solution vector with NaNs and than only overwrite the 
entries once.

I don't know if we have such a test for the general SolutionTransfer class. 
I will check that.

Marc

On Monday, December 28, 2020 at 1:39:33 PM UTC-7 Wolfgang Bangerth wrote:

> On 12/27/20 8:48 PM, Marc Fehling wrote:
> > 
> > 2) I did not know you were trying to interpolate a FENothing element 
> into a 
> > FEQ element. This should not be possible, as you can not interpolate 
> > information from simply 'nothing', and some assertion should be 
> triggered 
> > while trying to do so. The other way round should be possible, i.e., 
> > interpolation from FEQ to FENothing, since you will simply 'forget' what 
> has 
> > been on the old cell.
>
> In hindsight, FE_Nothing was maybe a poorly named class. It should really 
> have 
> been FE_Zero: A finite element space that contains only a single function 
> -- 
> the zero function. Because it only contains one function, it requires no 
> degrees of freedom.
>
> So interpolation from FE_Nothing to FE_Q is well defined if you take this 
> point of view, and projection from any finite element space to FE_Nothing 
> is also.
>
> Best
> Wolfgang
>
> -- 
> ------------------------------------------------------------------------
> Wolfgang Bangerth email: bang...@colostate.edu
> www: http://www.math.colostate.edu/~bangerth/
>
>

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