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A Finite Element Method for the Surface Biharmonic Problem without Stabilization or Piola Transforms — arXiv:2610.23492

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.23492
License (as archived): CC0-1.0
Archived: 2026-10-19T09:38:34.730Z
SHA-256 of the archived text: 81ec0c2940ba2c4fef68a11a873c52858b65695082f01e8c96b948e70b3d07e3
Stable URL of this page: https://metraipolis.com/documento/dc_8ed571dbffcb

How to cite

A Finite Element Method for the Surface Biharmonic Problem without Stabilization or Piola Transforms — arXiv:2610.23492 — arXiv (en), https://arxiv.org/abs/2610.23492 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_8ed571dbffcb (Metraipolis archive dc_8ed571dbffcb, sha256 81ec0c2940ba2c4fef68a11a873c52858b65695082f01e8c96b948e70b3d07e3)

BibTeX

@misc{dc8ed571dbffcb,
  title = {A Finite Element Method for the Surface Biharmonic Problem without Stabilization or Piola Transforms — arXiv:2610.23492},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.23492},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_8ed571dbffcb; sha256 81ec0c2940ba2c4fef68a11a873c52858b65695082f01e8c96b948e70b3d07e3},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.23492. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

For the biharmonic problem on closed smooth surfaces, we construct a nonconforming finite element method that requires neither stabilization nor the Piola transform. The reduced enriched quartic (REQ) element relies solely on vertex values and scalar edge moments. The same local construction applies to every triangle of a piecewise planar surface. The bilinear form consists of elementwise Laplacian inner products and permits standard finite element assembly. By separating the planar vertex residual from the angle defect contribution, we establish weak discrete Miranda--Talenti-type estimates on both planar meshes and closed piecewise planar surfaces. These estimates guarantee uniform stability on sufficiently refined interpolating surface meshes. We prove the well-posedness of the method, first-order convergence in the energy norm, and second-order convergence in the broken $H^1$ and $L^2$ norms. Numerical tests on three surfaces show the predicted convergence rates and examine the discrete Miranda--Talenti constants and angle defect scaling.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.NA, nuovi lavori del giorno).
Categorie arXiv: Numerical Analysis (math.NA).
Pagina del lavoro: https://arxiv.org/abs/2610.23492 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-19T09:34:29.800Z dalla pagina https://arxiv.org/list/math.NA/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).