@article{cdb6e482487747d78e5d1da99c3feec2,
title = "A fully discrete plates complex on polygonal meshes with application to the Kirchhoff–Love problem",
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.",
author = "{Di Pietro}, {Daniele A.} and Jerome Droniou",
note = "Funding Information: Received by the editor December 29, 2021, and, in revised form, May 2, 2022, and May 21, 2022. 2020 Mathematics Subject Classification. Primary 74K20, 74S05, 65N30. Key words and phrases. Discrete de Rham method, compatible discretisations, mixed formulation, plates complex, biharmonic equation, Kirchhoff–Love plates. The authors were supported by Agence Nationale de la Recherche through the grant ANR-20-MRS2-0004 “NEMESIS”. The first author was also supported by I-Site MUSE through the grant ANR-16-IDEX-0006 “RHAMNUS”. Publisher Copyright: {\textcopyright} 2022 American Mathematical Society",
year = "2023",
month = jan,
doi = "10.1090/mcom/3765",
language = "English",
volume = "92",
pages = "51--77",
journal = "Mathematics of Computation",
issn = "0025-5718",
publisher = "American Mathematical Society",
number = "339",
}