A construction of canonical nonconforming finite element spaces for elliptic equations of any order in any dimension
Year: 2025
Type: article
Abstract: A unified construction of canonical H m H^m -nonconforming finite elements is developed for n n -dimensional simplices for any m , n ≥ 1 m, n \geq 1 . Consistency with the Morley-Wang-Xu elements [Math. Comp. 82 (2013), pp. 25–43] is maintained when m ≤ n m \leq n . In the general case, the degrees of freedom and the shape function space exhibit well-matched multi-layer structures that ensure their alignment. Building on the concept of the nonconforming bubble function, the unisolvence is established using an equivalent integral-type representation of the shape function space and by applying induction on m m . The corresponding nonconforming finite element method applies to 2 m 2m -th order elliptic problems, with numerical results for m = 3 m=3 and m = 4 m=4 in 2D supporting the theoretical analysis.
Source: Mathematics of Computation
DOI: 10.1090/mcom/4142
Authors: Jia Li, Shuonan Wu
Institution: Peking University
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4413126977