2024/10/27 by Long Chen, Xuehai Huang, Chen, Long +1
Engineering · #58A10 #58J10 #65N30 #FOS: Mathematics #Numerical Analysis (math.NA) #Structural Analysis and Optimization #Structural Analysis of Composite Materials #Topology Optimization in Engineering
paper · pdf · doi:10.48550/arxiv.2410.20408
openalex publication_date 2024/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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. A geometric decomposition using newly defined bubble polynomial forms is also presented.