A fully discrete plates complex on polygonal meshes with application to the Kirchhoff–Love problem

Di Pietro, Daniele; Droniou, Jérôme

doi:10.1090/mcom/3765

A fully discrete plates complex on polygonal meshes with application to the Kirchhoff–Love problem
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Math. Comp. 92 (2023), 51-77 Request permission

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.

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