Work

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

Year: 2026

Type: preprint

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 $k\ge 0$ is the polynomial degree of the complex. Numerical experiments on polygonal meshes confirm the theoretical convergence rates.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.10150

Authors: Di Pietro, Daniele A., Droniou, Jérôme, Hu, Kaibo, Leroy, Arax

Institutions: Centre National de la Recherche Scientifique, Institut Montpelliérain Alexander Grothendieck, Monash University, University of Oxford

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: European Commission, Université de Montpellier

Awards: G3883331814, G5377794632

OpenAlex ID: W7212116962

Cites: 13

Cited by: 1

Related to: 10