A discrete de Rham method for the Reissner-Mindlin plate bending problem on polygonal meshes

TL;DR

This paper introduces a novel discretisation method for the Reissner--Mindlin plate bending problem on polygonal meshes, achieving high-order accuracy and being locking-free at the lowest order, validated through extensive numerical tests.

Contribution

It presents a new discrete de Rham-based method supporting general polygonal meshes and arbitrary order, with proven error estimates and locking-free performance at lowest order.

Findings

Error estimate of order h^{k+1} for general polynomial degree k

Locking-free error estimate for the lowest-order case k=0

Validated theoretical results with comprehensive numerical tests

Abstract

In this work we propose a discretisation method for the Reissner--Mindlin plate bending problem in primitive variables that supports general polygonal meshes and arbitrary order. The method is inspired by a two-dimensional discrete de Rham complex for which key commutation properties hold that enable the cancellation of the contribution to the error linked to the enforcement of the Kirchhoff constraint. Denoting by $k\ge 0$ the polynomial degree for the discrete spaces and by $h$ the meshsize, we derive for the proposed method an error estimate in $h^{k+1}$ for general $k$, as well as a locking-free error estimate for the lowest-order case $k=0$. The theoretical results are validated on a complete panel of numerical tests.