VTKFile to support printing HDivTrace functions

[adofarsi]

Describe the current issue
Would it be possible to extend VTKFile to support printing HDivTrace functions on facets?
Currently, the .write() method returns the following error from interpolation.py:
NotImplementedError: Can't interpolate onto traces, sorry.

Describe the solution you'd like
For example, printing such HDivTrace function for a triangular mesh would result in line elements, while for a tetrahedral mesh, it would produce triangular elements.

[dham]

I think if you use dmplex filter to extract the codimension 1 entities you can construct the skeleton mesh of a mesh. At that point you could just declare an appropriate DG field on that mesh and use cross-mesh interpolation. @ksagiyam may be able to advise on filtering the dmplex.

[adofarsi]

Thanks @dham! Being able to extract the skeleton mesh would be very helpful! Could you clarify how to interpolate HDivTrace functions into the skeleton mesh? Interpolation doesn't seem to be supported on such functions (NotImplementedError: Can't interpolate onto traces sorry). See: https://firedrakeproject.slack.com/archives/C1Q0Y6H8A/p1744766499792869

[dham]

OK, the first thing is that you want to project into Hdiv trace rather than interpolate.

To get from the volume mesh to the skeleton I think you just interpolate. Recall that it won't be HDiv trace on the skeleton but rather DG.

[pohlan]

I've also been struggling with this. Would you mind sharing your solution if you made it work? Thanks!

[adofarsi]

Hi @pohlan! Unfortunately I still haven’t found a solution. I’ll continue looking into it and let you know as soon as I make any progress.