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

TL;DR

This paper introduces a new fully discrete plates complex on polygonal meshes, enabling advanced numerical schemes for Kirchhoff-Love plates with proven stability and convergence, applicable to general polygonal element meshes.

Contribution

It develops a novel fully discrete plates complex based on the discrete de Rham paradigm, applicable to arbitrary polygonal meshes, and applies it to the Kirchhoff-Love problem with thorough analysis.

Findings

Stable and convergent numerical scheme for Kirchhoff-Love plates.

Applicable to meshes with general polygonal elements.

Extensive numerical tests validate the approach.

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.