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Raviart–Thomas

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Alternative namesRao–Wilton–Glisson, Nédélec (first kind) H(div)
Exterior calculus names\(\mathcal{P}^-_{k}\Lambda^{d-1}(\Delta_d)\)
Cockburn–fu names\(\left[S_{2,k}^\unicode{0x25FA}\right]_{d-1}\)
Abbreviated namesRT, RWG
Orders\(1\leqslant k\)
Reference elementstriangle, tetrahedron
Polynomial set\(\mathcal{P}_{k-1}^d \oplus \mathcal{Z}^{(15)}_{k}\)
↓ Show polynomial set definitions ↓
DOFsOn each facet: normal integral moments with an order \(k-1\) Lagrange space
On the interior of the reference element: integral moments with an order \(k-2\) vector Lagrange space
Number of DOFstriangle: \(k(k+2)\) (A005563)
tetrahedron: \(k(k+1)(k+3)/2\) (A077414)
Mappingcontravariant Piola
continuityComponents normal to facets are continuous
CategoriesVector-valued elements, H(div) conforming elements

Implementations

Basixbasix.ElementFamily.RT
↓ Show Basix examples ↓
Bempp"RWG" (triangle)
↓ Show Bempp examples ↓
Symfem"N1div"
↓ Show Symfem examples ↓
UFL"RT"
↓ 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 added30 December 2020
Element last updated02 August 2022