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arXiv · 2112.14497

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

Daniele A. Di Pietro·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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Daniele A. Di Pietro, Jérôme Droniou. 2021-12-29. A fully discrete plates complex on polygonal meshes with application to the Kirchhoff-Love problem. https://arxiv.org/abs/2112.14497

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