simplefem verification3 / 3

Last updated: 1 September 2026

simplefem is a simple Python finite library that is used as an example in the DefElement documantation. Its source code can be found at github.com/DefElement/simplefem.

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
Lagrange	triangle,1,equispaced
	triangle,2,equispaced
	triangle,3,equispaced

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/simplefem.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]