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

Jérôme Droniou
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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.
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Dates and versions

hal-03504496 , version 1 (29-12-2021)

Identifiers

  • HAL Id : hal-03504496 , version 1

Cite

Daniele Antonio Di Pietro, Jérôme Droniou. A fully discrete plates complex on polygonal meshes with application to the Kirchhoff-Love problem. 2021. ⟨hal-03504496⟩
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