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Analytical properties of polygonal Stokes and BGG Hessian complexes with application to Kirchhoff--Love plates

  • Daniele A. Di Pietro
  • Jérôme Droniou
  • Kaibo Hu
  • Arax Leroy
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Abstract

We develop and analyse a new arbitrary-order method for the Kirchhoff--Love plate problem on general polygonal meshes. The construction relies on a discrete Hessian complex obtained through the Bernstein--Gelfand--Gelfand construction, which stacks a Stokes complex on top of a tensorised de Rham complex. A key ingredient of the analysis is a detailed study of the former. We specifically establish primal and adjoint consistency estimates, as well as uniform Poincaré inequalities, and use these results to derive the analytical properties of the resulting discrete Hessian complex. The proposed method is then shown to be coercive and to converge with order k+1 with respect to the mesh size, where k≥ 0 is the polynomial degree of the complex. Numerical experiments on polygonal meshes confirm the theoretical convergence rates.

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Cite

BibTeXRIS
BibTeX
@misc{pietro2026analytical,
  title = {{Analytical properties of polygonal Stokes and BGG Hessian complexes with application to Kirchhoff--Love plates}},
  author = {Daniele A. Di Pietro and Jérôme Droniou and Kaibo Hu and Arax Leroy},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.10150},
  eprint = {2609.10150},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.10150},
}
RIS
TY  - UNPB
TI  - Analytical properties of polygonal Stokes and BGG Hessian complexes with application to Kirchhoff--Love plates
AU  - Daniele A. Di Pietro
AU  - Jérôme Droniou
AU  - Kaibo Hu
AU  - Arax Leroy
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.10150
UR  - https://arxiv.org/abs/2609.10150
AB  - We develop and analyse a new arbitrary-order method for the Kirchhoff--Love plate problem on general polygonal meshes. The construction relies on a discrete Hessian complex obtained through the Bernstein--Gelfand--Gelfand construction, which stacks a Stokes complex on top of a tensorised de Rham complex. A key ingredient of the analysis is a detailed study of the former. We specifically establish primal and adjoint consistency estimates, as well as uniform Poincaré inequalities, and use these results to derive the analytical properties of the resulting discrete Hessian complex. The proposed method is then shown to be coercive and to converge with order k+1 with respect to the mesh size, where k≥ 0 is the polynomial degree of the complex. Numerical experiments on polygonal meshes confirm the theoretical convergence rates.
ER  -