Hi Bruno -
Thank you for your fast reply. I'm sorry I'm not doing a great job of
explaining this. Here is an example from elasticity that illustrates what I
would like:
In this case there are displacement degrees of freedom at the nodes but the
stress is a quantity typically derived from the displacements. However, one
could make the stress an independent degree of freedom at the gauss points.

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So, in the element there would be displacement degrees of freedom at the
nodes and stress degrees of freedom at the gauss points. Does this make
sense?
Thank you again,
Jonathan
On Wednesday, March 7, 2018 at 10:30:44 AM UTC-5, Bruno Turcksin wrote:
>
> Jonathan,
>
> On Wednesday, March 7, 2018 at 10:20:44 AM UTC-5, Jonathan Russ wrote:
>>
>> Is there a FiniteElement in deal.II that allows the addition of degrees
>> of freedom at gauss points so that the DoFHandler object also manages them?
>> For example, I would like to have just a standard Lagrangian finite element
>> interpolated with the plain bilinear shape functions for nodal degrees of
>> freedom but I also have a single degree of freedom at each gauss point
>> within the element (and, consequently, residual equations at each gauss
>> point in each element). Is this possible in deal.II to have degrees of
>> freedom not associated with nodes?
>>
> I am not sure I understand your question. Do you want Lagrangian FE where
> you pick yourself the node? If that is the case then you can use this
> constructor
> <http://dealii.org/developer/doxygen/deal.II/classFE__Q.html#a32ccedfe518cfe3fca02cdddf9e664f6>
>
> Of course the order of the finite element will depend on the number of
> point in you quadrature. Or do you want to evaluate your finite element at
> some quadrature points?
>
> Best,
>
> Bruno
>
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