Higher-order Hermite on 1D manifolds - #240
Merged
Merged
Conversation
pbrubeck
force-pushed
the
pbrubeck/hermite-manifold
branch
2 times, most recently
from
March 26, 2026 14:29
2b68bac to
69073c8
Compare
pbrubeck
changed the title
This was referenced May 8, 2026
Hermite on intervals now takes any degree of at least three, adding point evaluations inside the edge, and accepts a variant for the points. On triangles and tetrahedra the degree must be three. On a manifold, the vertex derivative along the cell tangent flips with the cell orientation. The transformation for intervals uses the signed Jacobian determinant, which carries that orientation, so the element works on intervals embedded in higher dimensions. CubicHermite and CubicHermiteDualSet are renamed to Hermite and HermiteDualSet, since the element is no longer only cubic. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01NkPVBzACjxYBGb55Adz6Mu
pbrubeck
force-pushed
the
pbrubeck/hermite-manifold
branch
from
September 14, 2026 14:39
92c2f9c to
3901003
Compare
pbrubeck
marked this pull request as ready for review
September 14, 2026 14:42
rckirby
requested changes
Sep 15, 2026
rckirby
left a comment
rckirby
left a comment
There was a problem hiding this comment.
Looks fine to me? Just a comment on the comments.
rckirby
self-requested a review
September 15, 2026 20:17
rckirby
approved these changes
Sep 17, 2026
rckirby
left a comment
rckirby
left a comment
There was a problem hiding this comment.
Ok for now. Since we like knobs and completeness, it would be nice to have the full Ciarlet/Raviart Hermite family the simplex. Use cases there are limited, but it would be easy to add if needed.
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
2 participants
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
Description
Before this PR,
Hermiteon an interval was cubic only, and its basis transformation read the top-left block of the Jacobian. On an interval embedded in 2D or 3D, such as a 1DSubmeshof a surface, that block is one component of the edge vector. The transformation is then wrong for any edge that is not parallel to the first axis, and singular for an edge perpendicular to it.After this PR:
Hermiteon intervals accepts any degree of at least three. The extra degrees of freedom are point evaluations inside the edge, placed by the newvariantargument (default"gll"). On triangles and tetrahedra, any degree other than three raises aValueError.FIAT.CubicHermiteandCubicHermiteDualSetare renamed toFIAT.HermiteandHermiteDualSet, since the element is no longer only cubic.grad(u).n, so the cell tangent flips with the cell orientation, and the signed determinant carries that orientation. The element therefore works on intervals embedded in higher dimensions, given cell orientations on the mesh.The companion Firedrake change lets
init_cell_orientationsorient intervals embedded in 3D by a tangent direction, and tests the embedded Hermite element on an axis-aligned line and on a line perpendicular to the x axis.🤖 Generated with Claude Code
https://claude.ai/code/session_01NkPVBzACjxYBGb55Adz6Mu