an encyclopedia of finite element definitions

# Nédélec (second kind)

 Exterior calculus names $$\mathcal{P}_{k}\Lambda^{1}(\Delta_d)$$ Cockburn–fu names $$\left[S_{1,k}^\unicode{0x25FA}\right]_{1}$$ Abbreviated names N2curl Orders $$1\leqslant k$$ Reference elements triangle, tetrahedron Polynomial set $$\mathcal{P}_{k}^d$$↓ Show polynomial set definitions ↓ DOFs On 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 DOFs interval: $$k+1$$ (A000027)triangle: $$(k+1)(k+2)$$ (A002378)tetrahedron: $$(k+1)(k+2)(k+3)/2$$ (A027480) Mapping covariant Piola continuity Components tandential to facets are continuous Categories Vector-valued elements, H(curl) conforming elements

## Implementations

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

## Examples

 triangleorder 1 (click to view basis functions) triangleorder 2 (click to view basis functions) tetrahedronorder 1 (click to view basis functions) tetrahedronorder 2 (click to view basis functions)

## DefElement stats

 Element added 28 December 2020 Element last updated 02 August 2022