Submitted

Tangential Normal Decompositions of Finite Element Differential Forms

Long Chen and Xuehai Huang

Submitted

arXiv   Bibtex

ABSTRACT:

This paper introduces a novel tangential-normal (t-n)
decomposition for finite element differential forms, presenting a new
framework for constructing bases in finite element exterior
calculus. The main contribution is the development of a $t$-$n$ basis
where degrees of freedom and shape functions are explicitly dual, a
property that streamlines stiffness matrix assembly and enhances the
efficiency of interpolation and numerical integration. Additionally,
the integration of the well-documented Lagrange element basis supports
practical implementation of finite element differential forms in
applications.