The Zipped Finite Element Method: High-order shape functions for polygons

Computer Methods in Applied Mechanics and Engineering 2026 Open access

Read full text
Authors: Stefano Berrone, Lorenzo Neva, Moreno Pintore, Gioana Teora, Fabio Vicini
DOI: 10.1016/j.cma.2026.119060
Cited by: 0
References: 64

Abstract

In this paper, we present a new polygonal finite element method, called the Zipped Finite Element Method, for star-shaped polygons. The proposed approach constructs high-order shape functions as linear combinations of standard finite element basis functions defined on a local trivial sub-triangulation of each element. This refinement is used solely for the construction of the shape functions and does not affect the final number of degrees of freedom. The resulting finite element space includes polynomials of the desired order and preserves conformity across elements. Consequently, the method inherits the convergence properties of the finite element framework under suitable mesh assumptions. Numerical experiments confirm the expected rates of convergence.

Fields of Study & Subjects

Advanced Numerical Methods in Computational Mathematics Computational Geometry and Mesh Generation Topology Optimization in Engineering

Publication details

Journal / source
Computer Methods in Applied Mechanics and Engineering
Publisher
Elsevier BV
Volume
458
Pages
119060–119060
Publication date
16 May 2026
Language
EN