an encyclopedia of finite element definitions
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Abbreviated names | BR |
Orders | \(k=1\) |
Reference elements | triangle, tetrahedron |
Polynomial set | \(\mathcal{P}_{k}^d \oplus \mathcal{Z}^{(4)}_{k}\) (triangle) \(\mathcal{P}_{k}^d \oplus \mathcal{Z}^{(5)}_{k}\) (tetrahedron, \(k=1\)) \(\mathcal{P}_{k}^d \oplus \mathcal{Z}^{(6)}_{k}\) (tetrahedron, \(k=2\)) ↓ Show polynomial set definitions ↓ |
DOFs | On 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: integral moments of the divergence with an order \(0\) vector Lagrange space |
Number of DOFs | triangle: \(9\) tetrahedron: \(\begin{cases}16&k=1\\37&k=2\end{cases}\) |
Mapping | contravariant Piola |
continuity | Components normal to facets are continuous |
Categories | Vector-valued elements, H(div) conforming elements |
Symfem | "Bernardi-Raugel" ↓ Show Symfem 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) |
Element added | 19 April 2021 |
Element last updated | 02 August 2022 |