P1+P0 for pressure

General Discussion
1

Dear all,

I’m trying to implement an augmented Taylor-Hood method for mixed problems with a discontinuous pression finite element of the type P1+P0 (and not P1dc).
That anyone have a clue? I tried fespace Vh(Th, P1+P0) in vain.
Actually, P2b/P1dc generates too many degrees of freedom and for that reason I need to work with P2/P1+P0

Thanks!

2

Hi Amina
Can you provide a minimal working example, so that we can have a look at that make some suggestions to you.
IA

3

Actually my concern is only avout space declaring.
For Taylor-Hood in 2D we declare
Vh(Th,[P2,P2])
Ph(Th,P1)
and I just wanted to relace the P1 space by P1+P0, which doesn’t work. Hence, I was wondering if it is possible to do so differently. Actually, my space is the P1 space with addition of a constant to each cell (it is not the P1dc)

Best,
Amina.

4

Are you looking for P1 bubble finite element space ?
By the way, you can not use this FE space for pressure in order to the respect of the inf-sup condition

5

Hello Simon,
Thanks. I’m not looking for P1 bubble because the bubble is H1-conform, I’m looking for P1 with an additional constant onevery celle so that the pressure can be discontinuous. I don’t want to use P1dc because it ony works with P2b which generates much more degrees of freedom.
Best,
Amina.

6

Remark, you can use 2 pressures p = p0+p1 with p1 is P1 and p0 is P0
but in this case be careful because both space P1 and P0 have constant inside,
so you have to remove one pressure by adding term like

   int2d(Th)(epsilon*p0*q0)

where q = q1 + q0 are the tests function associated to p=p1+p0 and epsilon must be small enough but not to small.