[petsc-users] About Q3 tensor product Hermite element

[Matthew Knepley]

On Wed, Oct 5, 2022 at 4:39 PM Duan Junming via petsc-users <
petsc-users at mcs.anl.gov> wrote:

> Dear all,
>

I'm sorry. This email got lost in my inbox.


> I need to use Q3 tensor product Hermite element in 2D (point value,
> gradient, and mixed derivative at 4 vertices in a cell as unknowns).
>
> Is it available in PETSc FEM module now? I found that only Lagrange
> element is available.
>

We have elements that have moments and evaluations as dofs, so also Hdiv,
Hcurl, etc. However, you are right that we do not
have derivative dofs builtin. I have created them by hand before.


> If not, what is the correct path to implement Q3 tensor product Hermite
> element?
>
> I think I should create my own petscspace and petscdualspace?
>

You can probably use the PetscSpace polynomial class. You would need a
PetscDualSpace that used derivative dofs.
When I did this before, I just made an FD approximation with a quadrature
rule. Toby might have a nicer way to
differentiate the basis now.

> Or is there any package that has already provided this?
>
Firedrake has them, but only on simplices.

  Thanks,

     Matt


> Thanks for any suggestions!
>
>

-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener

https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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