> Oh yes, I actually did not assume my current way of doing things to work.
> After the static case was running, it was just a one liner (calling 
> set_fe_indices() again in each timestep) which was a really naive way of 
> doing 
> things.
> The problem at the moment is, that I just change the fe_index from pure 
> FE_Nothing to my actual FE_System without updating my sparsity pattern, and 
> re-initializing my matrices / vectors.
> To be honest I didn't even think, that this code runs in debug mode but 
> throws 
> an assertion, but it didn't...

Yes, this can't work. If you change the active_fe_index but not call 
distribute_dofs(), you will have inconsistent internal data structures. This 
won't work.


>     No, I would venture the guess that the cost of assembling and solving
>     linear systems is still the dominant factor. 
> 
> That's definitely right. Nevertheless I guess transferring old solutions with 
> no degrees of freedom on an ancient FE_Nothing cell to an updated version 
> where this cell has degrees of freedom might become tricky.

Well, you have to define how you want the solution that didn't exist on the 
empty cell to be interpreted if you actually have something on that cell now. 
I think that more than implementation, it's a question of what you *want* to 
happen.


> The problem with the second way is that just not using FE_Nothing but instead 
> my normal FE_System and setting all degrees of freedom to "0" on the former 
> FE_Nothing cells will not help either, since I use continuous elements and 
> don't want my interior ("0"-solid-solution) to interchange with my outer 
> (flow)-solution on the "cut-cells". I guess one way to overcome this issue is 
> to set all DoF on a "former FE_Nothing cell" to "0" besides the DoFs that 
> also 
> belong to a cut-cell neighbor?

That's exactly the question you have to answer first. What do you *want* to 
happen on these cells? If you know what you want to happen, we can talk about 
implementing it :-)

Best
  W.

-- 
------------------------------------------------------------------------
Wolfgang Bangerth          email:                 bange...@colostate.edu
                            www: http://www.math.colostate.edu/~bangerth/

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