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