Different solution with different Finite Elements (Linear - Quadratic)

[giannoko]

I am solving an 1D Poiseuille flow in cylindrical coordinates for velocity u and shear stress trz. I also impose a constant flow rate Q (defined by the Umean). The equations are written in normalized form. When I use P1-P1-R (MixedElement([FE1,FE1,FER])) elements, the solution is right, but when I use P2-P1-R (MixedElement([FE2,FE1,FER])) element the solution is wrong. Which is the problem?

[dokken]

I would strongly suggest you elaborate on what you mean by

@giannoko

element the solution is wrong

as it is not clear what you expect. Is the solver not converging, are your plots looking wrong etc?
Please also ready the guidlines in

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on how to get your question answered, as your code is far from a minimal example.

Please also note that you are using a fixed quadrature degree,

@giannoko

parameters["form_compiler"]["quadrature_degree"] = 3

which can cause problems for higher order spaces,as you then under-integrate the variational forms.

[giannoko]

This command parameters["form_compiler"]["quadrature_degree"] = 3 was the problem, now everything is fine.

However I will give more information about the problem so as no one will do it in the future. As I already stated, I get different solutions with Linear and Quadratic elements. I have no convergence issues. The code has excellent convergence in both cases. Additionally, there was no reason to give a sample of my code since I have no problem with any part of the code. I give you the whole code to see what I mean exactly. The solutions of the velocity profile for the two cases are

(Fig. 1)
P1 (velocity) - P1 (stress) - R (pressure gradient)
(Fig. 1)

(Fig. 2)
P2 (velocity) - P1 (stress) - R (pressure gradient)

The right solution is Fig. 1. According to @dokken, the command parameters["form_compiler"]["quadrature_degree"] = 3 can cause problems for higher order spaces. If I exclude this command I get exactly the same solution for both cases.