MULTIGRID METHODS FOR A STABILIZED REISSNER-MINDLIN PLATE FORMULATION

摘要

We consider a stabilized finite element formulation for the Reissner-Mindlin plate bending model. The method uses standard basis 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 mesh size and the thickness parameter. In order to apply the abstract multigrid theory, we introduce new interpolation norms and prove error estimates in them. Numerical results confirm the analysis.