H1-P0 FEM

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1

Hello everyone！

V = H1(mesh, order=0)
and
Vbar =H1(mesh, order=0, orderinner=0, dirichlet=[1,2,3,4])

Can these two finite element spaces be used？ and， do they have only one degree of freedom？

2

No the H1 space is only well defined for order >= 1. If you need a constant on the whole domain you can use the NumberSpace.
Best Christopher

3

Hi Christopher！

Now，can I define a constant on the skeleton？

Thanks！
Yongbin

4

The evaluator of the NumberSpace always returns the constant, so you should be able to use it in a skeleton formulation as well…
Did you try it?
Best
Christopher

5

Hi!
NumberSpace is the space V = FESpace(“number”,mesh) ?

Thanks！
Yongbin

6

Yes, better is the Python constructor: V = NumberSpace(mesh)
Best

7

Hi Christopher！

In my code， I have to use the space with dirichelet bounary
V = NumberSpace(mesh, dirichlet=[1,2,3,4)
,It’s still usable in my code, But I think it’s strange. because the trial function is only 0, namely V=0 .

Many thanks
Yongbin Han

8

Hi Yongbin,

using a NumberSpace together with Dirichlet boundaries does not make sense to me. The NumberSpace gives a singe scalar unknown (1 dof). If this scalar is then constrained to be zero at the boundary, it will simply be zero and there are no free dofs left over.

Best wishes,
Henry

9

Hi，Hvwahl！

Thank you very much！

Yongbin Han