Stabilized finite element approximations for the Reissner–Mindlin plate

Based on the Helmholtz decomposition of the transverse shear strain, Brezzi and Fortin in [5] introduced a three-stage algorithm for approximating the Reissner–Mindlin plate model with clamped boundary conditions and established uniform error estimates in the plate thickness. The first- and third-stage involve approximating two simple Poisson equations and the second-stage approximating a perturbed Stokes equation. Instead of using the mixed finite element method which is subject to the inf–sup condition, we consider a stabilized finite element approximation to such perturbed Stokes equations. Optimal error estimates independent of thickness of the plate are obtained for such equations. Then error analysis is established for the whole system.