Projection enhanced triangular finite element method
a novel FEM approach for polygonal elements
Abstract
In this work, we introduce the Projection Enhanced Triangular Finite Element Method (PET-FEM), a finite element formulation for polygonal meshes. The method relies on a FEM sub-mesh, while the internal degrees of freedom are recovered by a least-squares projection operator. This yields an implementation that is simple, flexible, and free of problem-dependent parameters. For higher-order PET-FEM, the formulation admits a serendipity-style reduction of internal degrees of freedom and shows improved robustness under mesh distortion compared to classical FEM serendipity elements. We further propose a first-order element that blends VEM and PET-FEM to obtain a computationally inexpensive, locking-free discretization. We benchmark our approach for the Poisson equation and for standard benchmarks in structural mechanics, including linear and nonlinear cases (e.g., Cook’s membrane and a punch test). The method achieves optimal convergence across all tests, with improved accuracy of the first-order element in locking-dominated problems.
Details
- Organisation(s)
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Institute of Continuum Mechanics
International RTG 2657: Computational Mechanics Techniques in High Dimensions
- Type
- Article
- Journal
- Computer Methods in Applied Mechanics and Engineering
- Volume
- 454
- ISSN
- 0045-7825
- Publication date
- 25.02.2026
- Publication status
- E-pub ahead of print
- Peer reviewed
- Yes
- ASJC Scopus subject areas
- Computational Mechanics, Mechanics of Materials, Mechanical Engineering, General Physics and Astronomy, Computer Science Applications
- Electronic version(s)
-
https://doi.org/10.1016/j.cma.2026.118838 (Access:
Open
)
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Details in the research portal "Research@Leibniz University"
