CMMSE: A Priori Verification Method for Curl-Conforming Basis Functions in Simplices

The construction of (hierarchical) curl-conforming basis functions has been a hot topic in the last decades in the finite element community. Especially, functions applied to simplices have been quite popular after the work by Nédélec in 1980. Many mixed-order and full-order families have been provided in the last years, but sometimes it is difficult to assess if they belong to the original space proposed by Nédélec (especially when orthogonalization procedures are applied). Here, a tool to determine if a family of basis functions belongs to the Nédélec space is provided. Since affine coordinates are the most frequent choice for simplices, particularities about its use with this kind of coordinates are detailed. A detailed survey of existing families is provided, and the practical application of the tool to a representative set of these families is discussed. The tool is also available for the community in a public repository.