Verification: full detail

Last updated: 16 October 2025

Element	Example	FIAT	Basix	Basix.UFL	NDElement
discontinuous Lagrange	interval,0,equispaced
	interval,1,equispaced
	interval,2,equispaced
	triangle,0,equispaced
	triangle,1,equispaced
	triangle,2,equispaced
	quadrilateral,0,equispaced
	quadrilateral,1,equispaced
	quadrilateral,2,equispaced
	tetrahedron,0,equispaced
	tetrahedron,1,equispaced
	tetrahedron,2,equispaced
	hexahedron,0,equispaced
	hexahedron,1,equispaced
	hexahedron,2,equispaced
	prism,0,equispaced
	prism,1,equispaced
	prism,2,equispaced
	pyramid,0,equispaced
	pyramid,1,equispaced
	pyramid,2,equispaced
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,0,lagrange
	triangle,1,lagrange
	triangle,0,legendre
	triangle,1,legendre
	quadrilateral,0,lagrange
	quadrilateral,1,lagrange
	quadrilateral,0,legendre
	quadrilateral,1,legendre
	tetrahedron,0,lagrange
	tetrahedron,1,lagrange
	hexahedron,0,lagrange
	hexahedron,1,lagrange
	prism,0,lagrange
	prism,1,lagrange
Raviart–Thomas	triangle,0,lagrange
	triangle,1,lagrange
	triangle,0,legendre
	triangle,1,legendre
	quadrilateral,0,lagrange
	quadrilateral,1,lagrange
	quadrilateral,0,legendre
	quadrilateral,1,legendre
	tetrahedron,0,lagrange
	tetrahedron,1,lagrange
	tetrahedron,0,legendre
	tetrahedron,1,legendre
	hexahedron,0,lagrange
	hexahedron,1,lagrange
	hexahedron,0,legendre
	hexahedron,1,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
	quadrilateral,1
	tetrahedron,1
	hexahedron,1
dPc	interval,1
	interval,2
	interval,3
	quadrilateral,1
	quadrilateral,2
	quadrilateral,3
Hellan–Herrmann–Johnson	triangle,0
	triangle,1
	triangle,2
	tetrahedron,0
	tetrahedron,1
	tetrahedron,2
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,2
	triangle,3
Bell	triangle,4
Bernardi–Raugel	triangle,1
	tetrahedron,1
	tetrahedron,2
Bernstein	interval,1
	interval,2
	interval,3
	triangle,1
	triangle,2
	triangle,3
Gopalakrishnan–Lederer–Schöberl	triangle,0
	triangle,1
	triangle,2
	tetrahedron,0
	tetrahedron,1
Guzmán–Neilan (first kind)	triangle,1
	tetrahedron,1
	tetrahedron,2
Guzmán–Neilan (second kind)	triangle,1
	tetrahedron,1
	tetrahedron,2
Hsieh–Clough–Tocher	triangle,3
Kong–Mulder–Veldhuizen	triangle,1
	triangle,2
	tetrahedron,1
Mardal–Tai–Winther	triangle,1
	tetrahedron,1
Morley	triangle,2
nonconforming Arnold–Winther	triangle,1
reduced Hsieh–Clough–Tocher	triangle,3
Taylor	interval,1
	interval,2
	interval,3
	triangle,1
	triangle,2
	triangle,3
trimmed serendipity H(curl)	quadrilateral,0
	quadrilateral,1
	quadrilateral,2
	hexahedron,0
	hexahedron,1
	hexahedron,2
trimmed serendipity H(div)	quadrilateral,0
	quadrilateral,1
	quadrilateral,2
	hexahedron,0
	hexahedron,1
	hexahedron,2
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.

Verification GitHub badges

Implementation	Badge	Markdown
FIAT		[](https://defelement.org/verification/fiat.html)
Basix		[](https://defelement.org/verification/basix.html)
Basix.UFL		[](https://defelement.org/verification/basix.ufl.html)
NDElement		[](https://defelement.org/verification/ndelement.html)
Symfem		[](https://defelement.org/verification/)