Two Classes of Mixed Finite Element Methods for the Reissner-Mindlin Plate Problem

In this paper, we propose mixed finite element methods for the Reissner-Mindlin Plate Problem by introducing the bending moment as an independent variable. We apply the finite element approximations of the stress field and the displacement field constructed for the elasticity problem by Hu (J Comp Math 33: 283–296, 2015), Hu and Zhang (arXiv:1406.7457, 2014) to solve the bending moment and the rotation for the Reissner-Mindlin Plate Problem. We propose two triples of finite element spaces to approximate the bending moment, the rotation, and the displacement. The feature of these methods is that they need neither reduction terms nor penalty terms. Then, we prove the well-posedness of the discrete problem and obtain the optimal estimates independent of the plate thickness. Finally, we present some numerical examples to demonstrate the theoretical results.