Rotating bases for finite element exterior calculus: closed-form change of basis under vertex permutations 6W9H24A378
| URI | m2://res/6W9H24A378 |
|---|---|
| Kind | preprint |
| Creators | Santiago Badia, Jordi Manyer, Antoine Marteau |
| Date | 2026-09-30 |
| MSC | 65-XX |
| Subjects | arxiv math.NA, arxiv cs.NA |
| Scope | in |
Expressions
e1: version, preprint
| Language | en |
|---|---|
| Date | 2026-09-30 |
| Ids | arXiv 2609.39511 |
Items in this resource
The mentions of the inventory that name this resource. Each name links to the card of its inventory row.
| Item | Kind | Where | Source |
|---|---|---|---|
| spanning set | definition | definition 5 | arxiv |
| spanning | statement | theorem 8 | arxiv |
| basis | statement | corollary 1 | arxiv |
| spanning | statement | theorem 2 | arxiv |
| filter characterisation | statement | theorem 3 | arxiv |
| directional catalogue | definition | definition 4 | arxiv |
| face ownership | statement | lemma 8 | arxiv |
| cardinality | statement | lemma 3 | arxiv |
| resummation identity | statement | theorem 4 | arxiv |
| two-term decomposition | statement | theorem 10 | arxiv |
| rotation of the directional catalogue | statement | theorem 5 | arxiv |
| conformity of the rotated bases | statement | corollary 8 | arxiv |
| same span and combinatorial inverse | statement | theorem 13 | arxiv |
| face ownership | statement | lemma 4 | arxiv |
| shift ratio | statement | lemma 10 | arxiv |
| rotation of the pair catalogue | statement | theorem 11 | arxiv |
| global identification | definition | definition 7 | arxiv |
| directional 1-form | definition | definition 1 | arxiv |
| spanning set | definition | definition 2 | arxiv |
| pullback of the basis functions | statement | theorem 12 | arxiv |
| pullback of the basis functions | statement | theorem 6 | arxiv |
| transformation matrix, Bernstein | statement | corollary 11 | arxiv |
| filter characterisation | statement | theorem 9 | arxiv |
| transformation matrix | statement | corollary 7 | arxiv |
| two-term decomposition, Bernstein | statement | corollary 9 | arxiv |
| cardinality | statement | lemma 7 | arxiv |
| dual basis | statement | lemma 9 | arxiv |
| basis filter | definition | definition 3 | arxiv |
| combinatorial inverse of the catalogue matrix | statement | corollary 3 | arxiv |
| pullback of the basis functions, Bernstein | statement | corollary 10 | arxiv |
| relabelling of barycentric monomials | statement | lemma 1 | arxiv |
| basis | statement | corollary 5 | arxiv |
| matrix form and sparsity | statement | corollary 6 | arxiv |
| matrix form and sparsity | statement | corollary 2 | arxiv |
| rotation of $\psi$ | statement | lemma 5 | arxiv |
| resummation of the directional forms | statement | lemma 2 | arxiv |
| triangle identity | statement | lemma 6 | arxiv |
| basis filter | definition | definition 6 | arxiv |
| transformation matrix | statement | corollary 4 | arxiv |
| same span and combinatorial inverse | statement | theorem 7 | arxiv |
| reduction of conformity to reference relabellings | statement | theorem 1 | arxiv |
Catalogue records
- arxiv: 2609.39511 (work)
- arxiv_text: 2609.39511 (work)