an encyclopedia of finite element definitions

# Nédélec (first kind)

 Alternative names Whitney (triangle,tetrahedron), Nédélec, Q H(curl) (quadrilateral,hexahedron), Raviart–Thomas cubical H(curl) (quadrilateral), Nédélec cubical H(curl) (hexahedron) De Rham complex families $$\left[S_{2,k}^\unicode{0x25FA}\right]_{1}$$ / $$\mathcal{P}^-_{k}\Lambda^{1}(\Delta_d)$$, $$\left[S_{4,k}^\square\right]_{1}$$ / $$\mathcal{Q}^-_{k}\Lambda^{1}(\square_d)$$ Abbreviated names N1curl, NC, RTce (quadrilateral), Nce (hexahedron) Variants Legendre: Integral moments are taken against orthonormal polynomialsLagrange: Integral moments are taken against (Lagrange)[element:lagrange] basis functions Orders $$1\leqslant k$$ Reference elements triangle, tetrahedron, quadrilateral, hexahedron, prism Polynomial set $$\mathcal{P}_{k-1}^d \oplus \mathcal{Z}^{(20)}_{k}$$ (triangle, tetrahedron) $$\mathcal{Q}_{k-1}^d \oplus \mathcal{Z}^{(21)}_{k}$$ (quadrilateral, hexahedron) ↓ Show polynomial set definitions ↓ DOFs On each edge: tangent integral moments with an order $$k-1$$ Lagrange space On each face (triangle): integral moments with an order $$k-2$$ vector Lagrange space On each face (quadrilateral): integral moments with an order $$k-1$$ Q H(div) space On each volume (tetrahedron): integral moments with an order $$k-3$$ vector Lagrange space On each volume (hexahedron): integral moments with an order $$k-1$$ Q H(div) space Number of DOFs triangle: $$k(k+2)$$ (A005563)tetrahedron: $$k(k+2)(k+3)/2$$ (A005564)quadrilateral: $$2k(k+1)$$ (A046092)hexahedron: $$3k(k+1)^2$$ (A059986)prism: $$3k(k+2)(k+1)/2$$ Mapping covariant Piola continuity Components tangential to facets are continuous Categories Vector-valued elements, H(curl) conforming elements

## Implementations

 Basix basix.ElementFamily.N1E↓ Show Basix examples ↓ This implementation is correct for all the examples below that it supports.↓ Show more ↓ Basix.UFL basix.ElementFamily.N1E↓ Show Basix.UFL examples ↓ This implementation is correct for all the examples below that it supports.↓ Show more ↓ Bempp "SNC"↓ Show Bempp examples ↓ FIAT FIAT.Nedelec(..., variant="integral")↓ Show FIAT examples ↓ This implementation is correct for all the examples below that it supports.↓ Show more ↓ Symfem "N1curl", variant="legendre" (triangle, Legendre; tetrahedron, Legendre)"Qcurl", variant="legendre" (quadrilateral, Legendre; hexahedron, Legendre)"Ncurl", variant="legendre" (prism, Legendre)"N1curl" (triangle, Lagrange; tetrahedron, Lagrange)"Qcurl" (quadrilateral, Lagrange; hexahedron, Lagrange)"Ncurl" (prism, Lagrange)↓ Show Symfem examples ↓ This implementation is used to compute the examples below and verify other implementations. (legacy) UFL "N1curl" (triangle, Lagrange; tetrahedron, Lagrange)"RTCE" (quadrilateral, Lagrange)"NCE" (hexahedron, Lagrange)↓ Show (legacy) UFL examples ↓

## Examples

 triangleorder 1Lagrange variant (click to view basis functions) triangleorder 2Lagrange variant (click to view basis functions) quadrilateralorder 1Lagrange variant (click to view basis functions) quadrilateralorder 2Lagrange variant (click to view basis functions) tetrahedronorder 1Lagrange variant (click to view basis functions) tetrahedronorder 2Lagrange variant (click to view basis functions) hexahedronorder 1Lagrange variant (click to view basis functions) hexahedronorder 2Lagrange variant (click to view basis functions) prismorder 1Lagrange variant (click to view basis functions) prismorder 2Lagrange variant (click to view basis functions) triangleorder 1Legendre variant (click to view basis functions) triangleorder 2Legendre variant (click to view basis functions) quadrilateralorder 1Legendre variant (click to view basis functions) quadrilateralorder 2Legendre variant (click to view basis functions)

## DefElement stats

 Element added 31 December 2020 Element last updated 16 September 2023