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Guzmán–Neilan (first kind)
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| Alternative names | Guzmán–Neilan |
| Abbreviated names | GN |
| Degrees | \(1\leqslant k\leqslant d-1\) where \(k\) is the Polynomial subdegree |
| Polynomial subdegree | \(k\) |
| Polynomial superdegree | \(d\) |
| Reference elements | triangle, tetrahedron |
| DOFs | On each vertex: point evaluations in coordinate direcions On each edge: (if \(k>1\)) point evaluations in coordinate directions at midpoints On each facet: normal integral moments with a degree \(0\) Lagrange space |
| Number of DOFs | triangle: \(9\) tetrahedron: \(\begin{cases}16&k=1\\34&k=2\end{cases}\) |
| Mapping | contravariant Piola |
| continuity | Function values are continuous. |
| Notes | This element is a modification of the Bernardi–Raugel element with the facet bubbles modified to be divergence free. |
| Categories | Vector-valued elements, Macro elements |
Implementations
This element is implemented in FIAT and Symfem .↓ Show implementation detail ↓Examples
| triangle degree 1 |  (click to view basis functions) |
| tetrahedron degree 1 |  (click to view basis functions) |
| tetrahedron degree 2 |  (click to view basis functions) |
References
- Guzmán, Johnny and Neilan, Michael. Inf-sup stable finite elements on barycentric refinements producing divergence-free approximations in arbitrary dimensions, SIAM Journal on Numerical Analysis 56, 2826–2844, 2018. [DOI: 10.1137/17M1153467] [BibTeX]
DefElement stats
| Element added | 01 August 2021 |
| Element last updated | 17 October 2024 |