Optimal $\mathcal{L}^2$ error bounds for MITC3 type element

Summary.

In this paper, we derive the optimal $\mathcal{L}^2$ error bounds for the stabilized MITC3 element [3], the MIN3 type element [7] and the T3BL element [8]. In this way we have solved the problem proposed recently in [5] in a positive manner. Moreover, we estimate the difference between stabilized MITC3 and MIN3 and show it is of order $\mathcal{O}(h^2)$ uniform in the plate thickness.