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PreprintCC BY-NC-ND 4.0arXiv

The Zipped Finite Element Method on polyhedral meshes

  • Stefano Berrone
  • Gioana Teora
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Abstract

We extend the high-order Zipped Finite Element Method to three-dimensional polyhedral elements. The construction relies on a local sub-tetrahedralization obtained by triangulating the polygonal faces and connecting the resulting vertices to a suitable interior point. High-order shape functions are constructed as linear combinations of standard finite element basis functions, with coefficients chosen to ensure exact polynomial reproduction on the faces and in the element interior while preserving global C0-conformity. We further introduce a QR-based strategy as a systematic alternative to the heuristic procedure that was adopted for the two-dimensional case. The QR-strategy is more systematic and robust than the heuristic strategy, while being independent of the spatial dimension and avoiding geometric alignment tests and problem-dependent tolerances. The resulting method is formulated for a diffusion-reaction problem and numerically assessed through three-dimensional convergence tests, confirming the expected optimal polynomial order of accuracy.

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Cite

BibTeXRIS
BibTeX
@misc{berrone2026zipped,
  title = {{The Zipped Finite Element Method on polyhedral meshes}},
  author = {Stefano Berrone and Gioana Teora},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.22955},
  eprint = {2609.22955},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.22955},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - The Zipped Finite Element Method on polyhedral meshes
AU  - Stefano Berrone
AU  - Gioana Teora
PY  - 2026
DA  - 2026/09/19
PB  - arXiv
DO  - 10.48550/arxiv.2609.22955
UR  - https://arxiv.org/abs/2609.22955
AB  - We extend the high-order Zipped Finite Element Method to three-dimensional polyhedral elements. The construction relies on a local sub-tetrahedralization obtained by triangulating the polygonal faces and connecting the resulting vertices to a suitable interior point. High-order shape functions are constructed as linear combinations of standard finite element basis functions, with coefficients chosen to ensure exact polynomial reproduction on the faces and in the element interior while preserving global C0-conformity. We further introduce a QR-based strategy as a systematic alternative to the heuristic procedure that was adopted for the two-dimensional case. The QR-strategy is more systematic and robust than the heuristic strategy, while being independent of the spatial dimension and avoiding geometric alignment tests and problem-dependent tolerances. The resulting method is formulated for a diffusion-reaction problem and numerically assessed through three-dimensional convergence tests, confirming the expected optimal polynomial order of accuracy.
ER  -