Bruno,

Hello everyone, I hope you are well.
> I have a quick question which I cannot seem to wrap my hear around. I 
> think it will sound confused, but anyway.
> Let's say I am solving for a scalar equation. I would have a 
> triangulation, then a DoFHandler and a FESystem with a multiplicity of one.
> I can loop over the cells and assemble my equations.
>
If you only have a scalar equation, there is no need to use FESystem but 
you can do that of course.
 

> Now, let's say I wanted to have an additional property that would be  a 
> vector defined at the nodes of my triangulation using the positions of the 
> nodes.
> However, this vector would not be used to be interpolated at the gauss 
> points, but would be use to cut the cells and do other geometric 
> manipulations.
> I could define another DoFHandler , and FESystem, but then when I loop 
> over the cells, there would be nothing to make sure that my DOF on both 
> equations are numbered in the same way.
> However, I cannot defined another vector using the FESystem of my scalar 
> equation, because the multiplicity is not the same.
> What would be the best way to proceed?
>
I am not quite sure to understand what you are asking for. The support 
points only coincide for FE_Q(1) elements with the nodes of the 
triangulation.
Normally, you would associate the entries of a Vector with the finite 
element vector defined by the degrees of freedom (and the ansatz space), 
but you can also store different information.
You are talking about two equations. What is the second equation and how is 
it related to the first one? Can you give an example how you want to use 
the Vectors?

Best,
Daniel

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