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Abbreviated names | BDFM |
Degrees | \(1\leqslant k\) where \(k\) is the Polynomial subdegree |
Polynomial subdegree | \(k\) |
Polynomial superdegree | \(k+1\) |
Lagrange subdegree | triangle: \(k\) tetrahedron: \(k\) quadrilateral: \(\operatorname{floor}((k+1)/d)\) hexahedron: \(\operatorname{floor}((k+1)/d)\) |
Lagrange superdegree | \(k+1\) |
Reference elements | triangle, quadrilateral, tetrahedron, hexahedron |
Polynomial set | \(\mathcal{Z}^{(10)}_{k+1}\) ↓ Show polynomial set definitions ↓ |
DOFs | On each facet (triangle): normal integral moments with a degree \(k\) Lagrange space On each facet (tetrahedron): normal integral moments with a degree \(k\) Lagrange space On each facet (quadrilateral): normal integral moments with a degree \(k\) dPc space On each facet (hexahedron): normal integral moments with a degree \(k\) dPc space On the interior of the reference element (triangle): integral moments with a degree \(k-1\) Nédélec (first kind) space On the interior of the reference element (tetrahedron): integral moments with a degree \(k-1\) Nédélec (first kind) space On the interior of the reference element (quadrilateral): integral moments with a degree \(k-1\) vector dPc space On the interior of the reference element (hexahedron): integral moments with a degree \(k-1\) vector dPc space |
Number of DOFs | triangle: \(k^2+5k+3\) quadrilateral: \((k+1)(k+4)\) (A028552) tetrahedron: \((k+2)(k^2+7k+4)/2\) hexahedron: \((k+1)(k+2)(k+6)/2\) |
Mapping | contravariant Piola |
continuity | Components normal to facets are continuous |
Categories | Vector-valued elements, H(div) conforming elements |
triangle degree 0 | ![]() (click to view basis functions) |
triangle degree 1 | ![]() (click to view basis functions) |
quadrilateral degree 0 | ![]() (click to view basis functions) |
quadrilateral degree 1 | ![]() (click to view basis functions) |
tetrahedron degree 0 | ![]() (click to view basis functions) |
tetrahedron degree 1 | ![]() (click to view basis functions) |
hexahedron degree 0 | ![]() (click to view basis functions) |
hexahedron degree 1 | ![]() (click to view basis functions) |
Element added | 30 January 2021 |
Element last updated | 31 March 2025 |