Multigrid Methods for a Stabilized Reissner-Mindlin Plate Formulation

We consider a stabilized finite element formulation for the Reissner-Mindlin plate bending model. The method uses standard bases functions for the deflection and the rotation vector. We apply a standard multigrid algorithm to obtain a preconditioner. We prove that the condition number of the preconditioned system is uniformly bounded with respect to the multigrid level and the thickness parameter. The abstract multigrid theory is applied for carefully chosen norms. We have to prove also some new finite element error estimates. Numerical results confirm the analysis.