an encyclopedia of finite element definitions
Verification
Last updated: 1 September 2026For 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:
| Verification passes from all the examples on the element's page | |
| Verification passes for some examples, but not all | |
| Verification fails for all examples |
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 |
| Basix |  | [](https://defelement.org/verification/basix.html) |
| Basix.UFL |  | [](https://defelement.org/verification/basix.ufl.html) |
| Ferrite.jl |  | [](https://defelement.org/verification/ferrite.html) |
| FIAT |  | [](https://defelement.org/verification/fiat.html) |
| ndelement |  | [](https://defelement.org/verification/ndelement.html) |
| Symfem |  | [](https://defelement.org/verification/) |
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]