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Nédélec (second kind)

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Exterior calculus names\(\mathcal{P}_{k}\Lambda^{1}(\Delta_d)\)
Cockburn–fu names\(\left[S_{1,k}^\unicode{0x25FA}\right]_{1}\)
Abbreviated namesN2curl
Orders\(1\leqslant k\)
Reference elementstriangle, tetrahedron
Polynomial set\(\mathcal{P}_{k}^d\)
↓ Show polynomial set definitions ↓
DOFsOn each edge: tangent integral moments with an order \(k\) Lagrange space
On each face: integral moments with an order \(k-1\) Raviart–Thomas space
On each volume: integral moments with an order \(k-2\) Raviart–Thomas space
Number of DOFsinterval: \(k+1\) (A000027)
triangle: \((k+1)(k+2)\) (A002378)
tetrahedron: \((k+1)(k+2)(k+3)/2\) (A027480)
Mappingcovariant Piola
continuityComponents tandential to facets are continuous
CategoriesVector-valued elements, H(curl) conforming elements

Implementations

Basixbasix.ElementFamily.N2E
↓ Show Basix examples ↓
Symfem"N2curl"
↓ Show Symfem examples ↓
UFL"N2curl"
↓ Show UFL examples ↓

Examples

triangle
order 1

(click to view basis functions)
triangle
order 2

(click to view basis functions)
tetrahedron
order 1

(click to view basis functions)
tetrahedron
order 2

(click to view basis functions)

References

DefElement stats

Element added28 December 2020
Element last updated02 August 2022