Nonconforming Quadrilateral Rotated $Q_1$ Element for Reissner-Mindlin Plate

Abstract

 In this paper, we extend two rectangular elements for Reissner-Mindlin plate [9] to the quadrilateral case. Optimal ${\rm H}^1$ and ${\rm L}^2$ error bounds independent of the plate thickness are derived under a mild assumption on the mesh partition.