an encyclopedia of finite element definitions
NDElement verification70 / 70
Last updated: 16 July 2025The 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 | |
| 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 | ||
| 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 | ||
| 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 | ||
| 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 |
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.
| 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/ndelement.html) |