A fully discrete plates complex on polygonal meshes with application to the Kirchhoff–Love problem
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- by Daniele A. Di Pietro and Jérôme Droniou;
- Math. Comp. 92 (2023), 51-77
- DOI: https://doi.org/10.1090/mcom/3765
- Published electronically: August 29, 2022
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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.References
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Bibliographic Information
- Daniele A. Di Pietro
- Affiliation: IMAG, Univ Montpellier, CNRS, Montpellier, France
- MR Author ID: 790640
- ORCID: 0000-0003-0959-8830
- Email: daniele.di-pietro@umontpellier.fr
- Jérôme Droniou
- Affiliation: School of Mathematics, Monash University, Melbourne, Australia
- MR Author ID: 655312
- ORCID: 0000-0002-3339-3053
- Email: jerome.droniou@monash.edu
- Received by editor(s): December 29, 2021
- Received by editor(s) in revised form: May 2, 2022, and May 21, 2022
- Published electronically: August 29, 2022
- Additional Notes: 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”
- © Copyright 2022 American Mathematical Society
- Journal: Math. Comp. 92 (2023), 51-77
- MSC (2020): Primary 74K20, 74S05, 65N30
- DOI: https://doi.org/10.1090/mcom/3765
- MathSciNet review: 4496959