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Mardal–Tai–Winther

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Abbreviated namesMTW
Orders\(k=3\)
Reference elementstriangle, tetrahedron
Polynomial set\(\mathcal{Z}^{(37)}_{k}\) (triangle)
\(\mathcal{P}_{k}^d \oplus \mathcal{Z}^{(38)}_{k}\) (tetrahedron)
↓ Show polynomial set definitions ↓
DOFsOn each facet (triangle): normal integral moments with an order \(1\) Lagrange space, and tangent integral moments with an order \(0\) Lagrange space

On each facet (tetrahedron): normal integral moments with an order \(1\) Lagrange space, and integral moments with an order \(1\) Nédélec (first kind) space
Number of DOFstriangle: \(9\)
tetrahedron: \(24\)
Mappingcontravariant Piola
continuityComponents normal to facets are continuous
CategoriesVector-valued elements, H(div) conforming elements

Implementations

Symfem"MTW"
↓ Show Symfem examples ↓
UFL"MTW" (triangle)
↓ Show UFL examples ↓

Examples

triangle
order 3

(click to view basis functions)
tetrahedron
order 3

(click to view basis functions)

References

DefElement stats

Element added09 January 2021
Element last updated02 August 2022