A fully discrete plates complex on polygonal meshes with application to the Kirchhoff-Love problem
Numerical Analysis
2021-12-30 v1 Numerical Analysis
Abstract
In this work we develop a novel fully discrete version of the plates complex, an exact Hilbert complex relevant for the mixed formulation of fourth-order problems. The derivation of the discrete complex follows the discrete de Rham paradigm, leading to an arbitrary-order construction that applies to meshes composed of general polygonal elements. The discrete plates complex is then used to derive a novel numerical scheme for Kirchhoff--Love plates, for which a full stability and convergence analysis are performed. Extensive numerical tests complete the exposition.
Keywords
Cite
@article{arxiv.2112.14497,
title = {A fully discrete plates complex on polygonal meshes with application to the Kirchhoff-Love problem},
author = {Daniele A. Di Pietro and Jérôme Droniou},
journal= {arXiv preprint arXiv:2112.14497},
year = {2021}
}