Element | Example | Basix | Basix.UFL | FIAT | NDElement |
Lagrange | interval,1,equispaced | | | | |
interval,2,equispaced | | | | |
interval,3,equispaced | | | | |
interval,1,gll | | | | |
interval,2,gll | | | | |
interval,3,gll | | | | |
interval,4,gll | | | | |
interval,1,lobatto | | | | |
interval,2,lobatto | | | | |
interval,3,lobatto | | | | |
triangle,1,equispaced | | | | |
triangle,2,equispaced | | | | |
triangle,3,equispaced | | | | |
quadrilateral,1,equispaced | | | | |
quadrilateral,2,equispaced | | | | |
quadrilateral,3,equispaced | | | | |
quadrilateral,1,gll | | | | |
quadrilateral,2,gll | | | | |
quadrilateral,1,lobatto | | | | |
quadrilateral,2,lobatto | | | | |
quadrilateral,3,lobatto | | | | |
tetrahedron,1,equispaced | | | | |
tetrahedron,2,equispaced | | | | |
hexahedron,1,equispaced | | | | |
hexahedron,2,equispaced | | | | |
hexahedron,1,lobatto | | | | |
hexahedron,2,lobatto | | | | |
prism,1,equispaced | | | | |
prism,2,equispaced | | | | |
pyramid,1,equispaced | | | | |
pyramid,2,equispaced | | | | |
Nédélec (first kind) | triangle,1,lagrange | | | | |
triangle,2,lagrange | | | | |
triangle,1,legendre | | | | |
triangle,2,legendre | | | | |
quadrilateral,1,lagrange | | | | |
quadrilateral,2,lagrange | | | | |
quadrilateral,1,legendre | | | | |
quadrilateral,2,legendre | | | | |
tetrahedron,1,lagrange | | | | |
tetrahedron,2,lagrange | | | | |
hexahedron,1,lagrange | | | | |
hexahedron,2,lagrange | | | | |
prism,1,lagrange | | | | |
prism,2,lagrange | | | | |
Raviart–Thomas | triangle,1,lagrange | | | | |
triangle,2,lagrange | | | | |
triangle,1,legendre | | | | |
triangle,2,legendre | | | | |
quadrilateral,1,lagrange | | | | |
quadrilateral,2,lagrange | | | | |
quadrilateral,1,legendre | | | | |
quadrilateral,2,legendre | | | | |
tetrahedron,1,lagrange | | | | |
tetrahedron,2,lagrange | | | | |
tetrahedron,1,legendre | | | | |
tetrahedron,2,legendre | | | | |
hexahedron,1,lagrange | | | | |
hexahedron,2,lagrange | | | | |
hexahedron,1,legendre | | | | |
hexahedron,2,legendre | | | | |
Brezzi–Douglas–Marini | triangle,1,lagrange | | | | |
triangle,2,lagrange | | | | |
triangle,1,legendre | | | | |
triangle,2,legendre | | | | |
tetrahedron,1,lagrange | | | | |
tetrahedron,2,lagrange | | | | |
tetrahedron,1,legendre | | | | |
tetrahedron,2,legendre | | | | |
bubble | interval,2 | | | | |
interval,3 | | | | |
triangle,3 | | | | |
triangle,4 | | | | |
Crouzeix–Raviart | triangle,1 | | | | |
dPc | interval,1 | | | | |
interval,2 | | | | |
interval,3 | | | | |
quadrilateral,1 | | | | |
quadrilateral,2 | | | | |
quadrilateral,3 | | | | |
Nédélec (second kind) | triangle,1,lagrange | | | | |
triangle,2,lagrange | | | | |
triangle,1,legendre | | | | |
triangle,2,legendre | | | | |
tetrahedron,1,lagrange | | | | |
tetrahedron,2,lagrange | | | | |
tetrahedron,1,legendre | | | | |
tetrahedron,2,legendre | | | | |
P1-iso-P2 | interval,1 | | | | |
triangle,1 | | | | |
quadrilateral,1 | | | | |
Regge | triangle,1 | | | | |
triangle,2 | | | | |
serendipity | interval,1 | | | | |
interval,2 | | | | |
interval,3 | | | | |
quadrilateral,1 | | | | |
quadrilateral,2 | | | | |
quadrilateral,3 | | | | |
Hermite | interval,3 | | | | |
triangle,3 | | | | |
tetrahedron,3 | | | | |
Alfeld–Sorokina | triangle,2 | | | | |
Argyris | triangle,5 | | | | |
Arnold–Winther | triangle,3 | | | | |
triangle,4 | | | | |
Bell | triangle,5 | | | | |
Bernardi–Raugel | triangle,1 | | | | |
tetrahedron,1 | | | | |
tetrahedron,2 | | | | |
Bernstein | interval,1 | | | | |
interval,2 | | | | |
interval,3 | | | | |
triangle,1 | | | | |
triangle,2 | | | | |
triangle,3 | | | | |
Brezzi–Douglas–Fortin–Marini | triangle,1 | | | | |
triangle,2 | | | | |
quadrilateral,1 | | | | |
quadrilateral,2 | | | | |
tetrahedron,2 | | | | |
hexahedron,2 | | | | |
Guzmán–Neilan (first kind) | triangle,1 | | | | |
tetrahedron,1 | | | | |
tetrahedron,2 | | | | |
Guzmán–Neilan (second kind) | triangle,1 | | | | |
tetrahedron,1 | | | | |
tetrahedron,2 | | | | |
Hellan–Herrmann–Johnson | triangle,1 | | | | |
triangle,2 | | | | |
Hsieh–Clough–Tocher | triangle,3 | | | | |
Kong–Mulder–Veldhuizen | triangle,1 | | | | |
triangle,2 | | | | |
tetrahedron,1 | | | | |
Mardal–Tai–Winther | triangle,3 | | | | |
tetrahedron,3 | | | | |
Morley | triangle,2 | | | | |
nonconforming Arnold–Winther | triangle,2 | | | | |
reduced Hsieh–Clough–Tocher | triangle,3 | | | | |
Taylor | interval,1 | | | | |
interval,2 | | | | |
interval,3 | | | | |
triangle,1 | | | | |
triangle,2 | | | | |
triangle,3 | | | | |
trimmed serendipity H(curl) | quadrilateral,1 | | | | |
quadrilateral,2 | | | | |
quadrilateral,3 | | | | |
hexahedron,1 | | | | |
hexahedron,2 | | | | |
hexahedron,3 | | | | |
trimmed serendipity H(div) | quadrilateral,1 | | | | |
quadrilateral,2 | | | | |
quadrilateral,3 | | | | |
hexahedron,1 | | | | |
hexahedron,2 | | | | |
hexahedron,3 | | | | |
vector dPc | quadrilateral,1 | | | | |
quadrilateral,2 | | | | |
quadrilateral,3 | | | | |
hexahedron,1 | | | | |
hexahedron,2 | | | | |
vector Lagrange | triangle,1 | | | | |
triangle,2 | | | | |
tetrahedron,1 | | | | |
tetrahedron,2 | | | | |
vector Q | quadrilateral,1 | | | | |
quadrilateral,2 | | | | |
hexahedron,1 | | | | |
hexahedron,2 | | | | |
For each element in the table above, the verification test passes for an example if:
- The element's basis functions span the same space as Symfem.
- The number of DOFs associated with each sub-entity of the cell is the same as Symfem.
- The element has the same continuity between cells as Symfem.
The symbols in the table have the following meaning:
| Verification passes |
| Verification fails |
| Example not implemented |
You can view a summarised version of this information on the
verification page.
The verification data is also available
in JSON format.
Implementation | Badge | Markdown |
Basix | | [![DefElement verification](https://defelement.org/badges/basix.svg)](https://defelement.org/verification.html) |
Basix.UFL | | [![DefElement verification](https://defelement.org/badges/basix.ufl.svg)](https://defelement.org/verification.html) |
Symfem | | [![DefElement verification](https://defelement.org/badges/symfem.svg)](https://defelement.org/verification.html) |
FIAT | | [![DefElement verification](https://defelement.org/badges/fiat.svg)](https://defelement.org/verification.html) |
NDElement | | [![DefElement verification](https://defelement.org/badges/ndelement.svg)](https://defelement.org/verification.html) |