English

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}
}