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

In this work we develop a novel fully discrete version of the plates complex, an exact Hilbert complex relevant for mixed formulation fourth-order problems. The derivation follows de Rham paradigm, leading to arbitrary-order construction that applies meshes composed general polygonal elements. is then used derive numerical scheme Kirchhoff–Love plates, which full stability and convergence analysis are performed. Extensive tests complete exposition.