Verification

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 algorithm used to perform verification is described in detail in the DefElement paper^[1].

The symbols in the table have the following meaning:

You can view more details of which examples pass and fail on the verification with full detail 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)
NDElement		[](https://defelement.org/verification/ndelement.html)
Symfem		[](https://defelement.org/verification/)
Basix.UFL		[](https://defelement.org/verification/basix.ufl.html)

References

• [1] Scroggs, Matthew W. and Brubeck, Pablo D. and Dean, Joseph P. and Dokken, Jørgen S. and Marsden, India. DefElement: an encyclopedia of finite element definitions, submitted to Computational Science and Engineering, 2025. [DOI: 10.48550/arXiv.2506.20188]