A Robust Discretization of the Reissner-Mindlin Plate with Arbitrary Polynomial Degree

Abstract

A numerical scheme for the Reissner–Mindlin plate model is proposed. The method is based on a discrete Helmholtz decomposition and can be viewed as a generalization of the nonconforming finite element scheme of Arnold and Falk [SIAM J. Numer. Anal., 26(6):1276-1290, 1989]. The two unknowns in the discrete formulation are the in-plane rotations and the gradient of the vertical displacement. The decomposition of the discrete shear variable leads to equivalence with the usual Stokes system with penalty term plus two Poisson equations and the proposed method is equivalent to a stabilized discretization of the Stokes system that generalizes the Mini element. The method is proved to satisfy a best-approximation result which is robust with respect to the thickness parameter $t$.