DefElement: an encyclopedia of finite element definitions

Journal article

DefElement is an online encyclopedia of finite element definitions that was created and is maintained by the authors of this paper. DefElement aims to make information about elements defined in the literature easily available in a standard format. There are a number of open-source finite element libraries available, and it can be difficult to check that an implementation of an element in a library matches the element’s definition in the literature or implementation in another library, especially when many libraries include variants of elements whose basis functions do not match exactly. In this paper, we carefully derive conditions under which elements can be considered equivalent and describe an algorithm that uses these conditions to verify that two implementations of a finite element are indeed variants of the same element. The results of scheduled runs of our implementation of this verification algorithm are included in the information available on the DefElement website.

Authors: Scroggs, MW; Brubeck, PD; Dean, JP; Dokken, JS; Marsden, I

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Computational Science and Engineering
• Volume: 3
• Issue: 1
• Article number: 2
• Publication date: 2026-04-14
• Acceptance date: 2026-03-11
• DOI: 10.1007/s44207-026-00011-0
• EISSN: 2948-1597
• ISSN: 2948-1597
• Language: English
• Keywords: Finite element methods