The Zipped Finite Element Method: High-order Shape Functions for Polygonal Elements

  • Berrone, Stefano (Politecnico di Torino)
  • Neva, Lorenzo (Politecnico di Torino)
  • Pintore, Moreno (Sorbonne Université, Inria)
  • Teora, Gioana (Politecnico di Torino)
  • Vicini, Fabio (Politecnico di Torino)

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In this presentation, we introduce the Zipped Finite Element Method (Z-FEM), a novel high-order polygonal finite element method designed for general star-shaped polygonal meshes. The proposed approach constructs conforming high-order shape functions as a weighted combination of standard FEM basis functions defined on a local sub-triangulation of each polygonal element. Several numerical experiments are presented to validate the proposed method. The results confirm the exact polynomial reproduction, demonstrate optimal convergence rates in standard error norms, and highlight the accuracy of Z-FEM on general polygonal meshes.