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# 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) Exterior calculus names $$\mathcal{P}^-_{k}\Lambda^{1}(\Delta_d)$$, $$\mathcal{Q}^-_{k}\Lambda^{1}(\square_d)$$ Cockburn–fu names $$\left[S_{2,k}^\unicode{0x25FA}\right]_{1}$$, $$\left[S_{4,k}^\square\right]_{1}$$ Abbreviated names N1curl, NC, RTce (quadrilateral), Nce (hexahedron) Orders $$1\leqslant k$$ Reference elements triangle, tetrahedron, quadrilateral, hexahedron, prism Polynomial set $$\mathcal{P}_{k-1}^d \oplus \mathcal{Z}^{(35)}_{k}$$ (triangle, tetrahedron) $$\mathcal{Q}_{k-1}^d \oplus \mathcal{Z}^{(36)}_{k}$$ (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 tandential to facets are continuous Categories Vector-valued elements, H(curl) conforming elements

## Implementations

 Basix basix.ElementFamily.N1E (triangle, tetrahedron, quadrilateral, hexahedron)↓ Show Basix examples ↓ Bempp "SNC" (triangle)↓ Show Bempp examples ↓ Symfem "N1curl" (triangle, tetrahedron)"Qcurl" (quadrilateral, hexahedron)"Ncurl" (prism)↓ Show Symfem examples ↓ UFL "N1curl" (triangle, tetrahedron)"RTCE" (quadrilateral)"NCE" (hexahedron)↓ Show UFL examples ↓

## Examples

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

## DefElement stats

 Element added 30 December 2020 Element last updated 02 August 2022