On Wed, Oct 5, 2022 at 4:39 PM Duan Junming via petsc-users < [email protected]> 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/>