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Huang–Zhang

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Alternative names\(Q_{k+1,k}\times Q_{k,k+1}\)
Abbreviated namesHZ
Orders\(2\leqslant k\)
Reference elementsquadrilateral
Polynomial set\(\mathcal{Z}^{(12)}_{k} \oplus \mathcal{Z}^{(13)}_{k}\)
↓ Show polynomial set definitions ↓
DOFsOn each facet: normal integral moments with an order \(k-1\) Lagrange space, and tangent integral moments with an order \(k-2\) Lagrange space
On the interior of the reference element: integral moments with \(\left\{\left(\begin{array}{c}x^iy^j\\0\end{array}\right)\middle|i\in\{0,1,...,k-1\}, j\in\{0,1,...,k-2\}\right\}\cup\left\{\left(\begin{array}{c}x^iy^j\\0\end{array}\right)\middle|i\in\{0,1,...,k-2\}, j\in\{0,1,...,k-1\}\right\}\)
Number of DOFsquadrilateral: \(2k(k+1)\) (A046092)
Mappingcontravariant Piola
continuityComponents normal to facets are continuous
CategoriesVector-valued elements, H(div) conforming elements

Implementations

Symfem"HZ"
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Examples

quadrilateral
order 2
(click to view basis functions)
quadrilateral
order 3
(click to view basis functions)

References

DefElement stats

Element added09 December 2022
Element last updated09 December 2022