Hello,
I want to solve an 1D Poiseuille flow by imposing a constant volumetric flow rate. So the question is how can I define a global unknown like flow rate (unknown that has no spatial distribution) to my problem? Is there any special case in Fenics that treats unknowns that are not written on any mesh vertex?
Thank you
Yes, there is an element type "Real" that can be used for a single global degree of freedom in \mathbb{R}. Take a look at the pure Neumann BC Poisson equation demo, where such an unknown is used as a global Lagrange multiplier, to enforce that the average solution is zero.
Thank you very much Kamensky. This is what I want.
Hello Kamensky,
I understand how to introduce a constraint like this one involved in Neumann BC Poisson equation demo but I cannot understand how to impose a total flow rate through the integral 
where Uz,m is the mean velocity at the inlet.
Thank you