an encyclopedia of finite element definitions
Basix verification116 / 116
Last updated: 1 January 2026The 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 | |
| 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 | ||
| 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 | ||
| dPc | quadrilateral,1 | |
| quadrilateral,2 | ||
| quadrilateral,3 | ||
| Hellan–Herrmann–Johnson | triangle,0 | |
| triangle,1 | ||
| triangle,2 | ||
| tetrahedron,0 | ||
| tetrahedron,1 | ||
| tetrahedron,2 | ||
| Hermite | interval,3 | |
| triangle,3 | ||
| tetrahedron,3 | ||
| Lagrange | interval,1,equispaced | |
| interval,2,equispaced | ||
| interval,3,equispaced | ||
| interval,1,gll | ||
| interval,2,gll | ||
| interval,3,gll | ||
| interval,4,gll | ||
| triangle,1,equispaced | ||
| triangle,2,equispaced | ||
| triangle,3,equispaced | ||
| quadrilateral,1,equispaced | ||
| quadrilateral,2,equispaced | ||
| quadrilateral,3,equispaced | ||
| quadrilateral,1,gll | ||
| quadrilateral,2,gll | ||
| tetrahedron,1,equispaced | ||
| tetrahedron,2,equispaced | ||
| hexahedron,1,equispaced | ||
| hexahedron,2,equispaced | ||
| 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 | ||
| 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 | ||
| 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 | ||
| Regge | triangle,1 | |
| triangle,2 | ||
| serendipity | interval,1 | |
| interval,2 | ||
| interval,3 | ||
| quadrilateral,1 | ||
| quadrilateral,2 | ||
| quadrilateral,3 |
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:
| Verification passes | |
| Verification fails |
You can information about verification of other libraries on the verification page.
Verification Github badge
| Badge | Markdown |
 | [](https://defelement.org/verification/basix.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]