AN hp ERROR ANALYSIS OF MITC PLATE ELEMENTS

We give an hp error analysis of several rectangular families of finite elements for the Reissner–Mindlin plate bending equations. We consider both the original MITC families [K. J. Bathe, F. Brezzi, and M. Fortin, Internat. J. Numer. Methods Engrg., 28 (1989), pp. 1787– 1801] and some new ones introduced in this paper. For the deflection and rotation we give error estimates which are optimal with respect to the mesh size h and optimal up to O(kε), ε > 0 arbitrary, with respect to the polynomial degree k. We also obtain estimates for the error in the shear force, calculated via two different methods. Our analysis utilizes some recent results of ours for the mixed method for the Stokes problem, as well as hp interpolation estimates for mixed methods for secondorder elliptic equations. In this regard, we derive new hp results in this paper for the Brezzi–Douglas– Fortin–Marini spaces and improve upon previous estimates for the Brezzi–Douglas–Marini spaces.