Is it possible to apply periodic condition on a FiniteElement Space (Mixed Formulation)

variational formulation
1

Hi,

I would like to constrain (periodicaly) a subdomain of a FunctionSpace define like

V = VectorElement("CG", mesh.ufl_cell(), 2)
Q = FiniteElement("CG", mesh.ufl_cell(), 1)
TH = V * Q
W = FunctionSpace(mesh, TH)

It doesn’t seem possible to constrain Q (with the FiniteElement syntax) as for the syntax “Function space” syntax (see : https://fenicsproject.org/qa/5279/periodic-boundaries-and-mixed-formulation-poisson-equation/)?
I tried
Q = FiniteElement("CG", mesh.ufl_cell(), 1, constrained_domain=PeriodicBoundary1())
but it doesn’t work.

Is there a way to constrain Q = W.sub(1) directly in the definition of W ?

Thank you in advance for your answer

2

By design creating a mixed space where only one of the variables is periodic is not supported in dolfin. You can check this discussion (if I understand your question correctly).

Instead of creating a MixedFunctionSpace, you could create a block system from scratch (I have never tested this though) or use this approach.

3

Thank you very much for your answer. That’s exactly what I’m trying to do.

Maybe I’m going wrong in the resolution of my problem.

I would like your opinion on how to implement my system of equations on Fenics.

I solve a darcy mixed formulation

u = -K/mu*grad( p )
div(u)=0

(so as to keep the incompressibility, that I could lose with a resolution of a simple pressure equation -div ( Kgrad( p ) ) = 0) on a square with the boundaries conditions :
SquareCLperiodic

I take (G1, G2) = (1,0).

I end up with a periodic pressure in the horizontal and a vertical pressure gradient. So, I need a first periodicity on Q (my space pressure).
Then, the conditions on the Darcy’s velocity ask (as I am on a square ie without curvatures: I know well the form of my normals n_i) a periodicty on W.sub (0).sub (0) to the horizontal and on W.sub (0).sub (1) verticaly (where W.sub (0) = V is the velocity space).

So, It seems that I can not force the periodicity horizontally and vertically directly on my space W = V*Q .

Thank you