Dear deal.ii community,

I have a question regarding a simple heat equation. Assuming we have the 
following equation
[image: heat_equation.png].

Is there a way to compute the actual numeric value of [image: dudt.png] at 
the quadrature points given the solution vector u? My first idea was to use 
quadratic elements and then just use FEValues.get_function_hessians() with 
the solution u, which seems to work. I was wondering if it is also somehow 
possible to use linear elements. For example, when multiplying by a test 
function w and doing integration by parts on the right hand side to shift 
one derivative to the test function. Would there be a way to evaluate this 
new expression to get [image: dudt.png]? Or would this then give me [image: 
w_dudt.png]?

This is more of a theoretical question, but any comments or hints would be 
appreciated!

Best,
Johanna

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