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
- Organisationseinheit(en)
-
Institut für Kontinuumsmechanik
Internationales GRK 2657: Methoden der Numerischen Mechanik in höheren Dimensionen
- Typ
- Artikel
- Journal
- Computer Methods in Applied Mechanics and Engineering
- Band
- 454
- ISSN
- 0045-7825
- Publikationsdatum
- 25.02.2026
- Publikationsstatus
- Elektronisch veröffentlicht (E-Pub)
- Peer-reviewed
- Ja
- ASJC Scopus Sachgebiete
- Numerische Mechanik, Werkstoffmechanik, Maschinenbau, Allgemeine Physik und Astronomie, Angewandte Informatik
- Elektronische Version(en)
-
https://doi.org/10.1016/j.cma.2026.118838 (Zugang:
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)
