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arXiv · 2507.17333

Design and homological analysis of twisted and BGG Stokes-de Rham complexes on polygonal meshes

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

We design a discrete Bernstein--Gelfand--Gelfand (BGG) diagram in a two-dimensional setting on polygonal meshes based on the DDR framework; the diagram is made of a discrete Stokes polygonal complex and a tensorised Discrete de Rham complex, and the BGG construction leads to novel twisted and Hessian complexes applicable on generic polygonal meshes; such complexes enable, in particular, discretisations of plate problems. Complete homological properties of the discrete Stokes complex and of the complexes built from the BGG diagram are established.

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Daniele A. Di Pietro, Jérôme Droniou, Kaibo Hu, Arax Leroy. 2025-07-23. Design and homological analysis of twisted and BGG Stokes-de Rham complexes on polygonal meshes. https://arxiv.org/abs/2507.17333

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