FIAT verification122 / 131

Last updated: 1 July 2025

The plot above shows the number of elements passing verificiation (green line) out of the number of elements being verified (dashed black line) over time.

Element	Example
Alfeld–Sorokina	triangle,2
Argyris	triangle,5
Arnold–Winther	triangle,2
Bell	triangle,4
Bernardi–Raugel	triangle,1
	tetrahedron,1
	tetrahedron,2
Bernstein	interval,1
	interval,2
	interval,3
	triangle,1
	triangle,2
	triangle,3
Brezzi–Douglas–Marini	triangle,1,legendre
	triangle,2,legendre
	tetrahedron,1,legendre
	tetrahedron,2,legendre
bubble	interval,2
	interval,3
	triangle,3
	triangle,4
Crouzeix–Raviart	triangle,1
	tetrahedron,1
discontinuous Lagrange	interval,0,equispaced
	interval,1,equispaced
	interval,2,equispaced
	triangle,0,equispaced
	triangle,1,equispaced
	triangle,2,equispaced
	tetrahedron,0,equispaced
	tetrahedron,1,equispaced
	tetrahedron,2,equispaced
dPc	interval,1
	interval,2
	interval,3
	quadrilateral,1
	quadrilateral,2
	quadrilateral,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
Hellan–Herrmann–Johnson	triangle,0
	triangle,1
	triangle,2
	tetrahedron,0
	tetrahedron,1
	tetrahedron,2
Hermite	interval,3
	triangle,3
	tetrahedron,3
Hsieh–Clough–Tocher	triangle,3
Kong–Mulder–Veldhuizen	triangle,1
	triangle,2
	tetrahedron,1
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
	tetrahedron,1,equispaced
	tetrahedron,2,equispaced
Mardal–Tai–Winther	triangle,1
Morley	triangle,2
Nédélec (first kind)	triangle,0,lagrange
	triangle,1,lagrange
	triangle,0,legendre
	triangle,1,legendre
	tetrahedron,0,lagrange
	tetrahedron,1,lagrange
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
nonconforming Arnold–Winther	triangle,1
P1-iso-P2	interval,1
	triangle,1
Raviart–Thomas	triangle,0,lagrange
	triangle,1,lagrange
	triangle,0,legendre
	triangle,1,legendre
	tetrahedron,0,lagrange
	tetrahedron,1,lagrange
	tetrahedron,0,legendre
	tetrahedron,1,legendre
reduced Hsieh–Clough–Tocher	triangle,3
Regge	triangle,1
	triangle,2
serendipity	interval,1
	interval,2
	interval,3
	quadrilateral,1
	quadrilateral,2
	quadrilateral,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

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

You can information about verification of other libraries on the verification page.

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