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Guzmán–Neilan

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Abbreviated namesBR
Orders\(k=1\)
Reference elementstriangle, tetrahedron
DOFsOn each edge: (if \(k>1\)) point evaluations in tangential directions at midpoints
On each facet: point evaluations in normal directions at vertices,
normal integral moments with an order \(k-1\) Lagrange space, and (if \(k>1\)) point evaluations in normal directions at midpoints of edges
On the interior of the reference element: , and point evaluations at the midpoint
Number of DOFstriangle: \(11\)
tetrahedron: \(\begin{cases}19&k=1\\49&k=2\end{cases}\)
Mappingcontravariant Piola
continuityComponents normal to facets are continuous
NotesThis element is a modification of the Bernardi–Raugel element with the facet bubbles modified to be divergence free.
CategoriesVector-valued elements, H(div) conforming elements

Implementations

Symfem"Guzman-Neilan"
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Examples

triangle
order 1

(click to view basis functions)
tetrahedron
order 1

(click to view basis functions)
tetrahedron
order 2

(click to view basis functions)

References

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Element added01 August 2021
Element last updated02 August 2022