gridap / gridap/GridapP4est.jl

[FESpaces on Trians] Integration on GhostSkeleton

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Hi, @amartinhuertas,

(This is the brief follow-up I promised on the discussion in our last meeting 19/11/25).

Other than integrating on the active portion of the skeleton triangulation (for DG), we will also need to integrate on the ghost skeleton.

In GE, the ghost skeleton on uniform grids is generated by restricting the SkeletonTriangulation to the set of faces that are between CUT and CUT cells or CUT and ACTIVE cells, as seen [here](https://github.com/gridap/GridapEmbedded.jl/blob/3d9a39651b0ab8f55962c791c126e62bacf3a547/src/Interfaces/EmbeddedDiscretizations.jl#L514).

This requires both the conforming and non-conforming connectivity information from faces to cells. If we only use the conforming part, we miss faces that belong to the ghost skeleton (e.g., below I show the incomplete ghost skeleton in pink (*) and the boundary in white on a p4est mesh).

(*) Remark: Only searching the faces between cut cells. I will update the drawing with the ones between cut and active whenever I have some time.

Image

Of course, using the complete connectivity information, I recover the complete GhostSkeleton (not showing it here, but I have already implemented it).

This raises the question: Should we also be able to generate portions of SkeletonTriangulations from p4est meshes (with the conforming + non-conforming grid topology) or can we integrate on the ghost skeleton by reusing the code that you're working on to give support to DG?

If anything is not clear, please let me know.

Thank you so much!

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