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 conside r both the original MITC families [K. J. Bathe, F. Brezzi, and M. Fort in, Internat. J. Numer. Methods Engrg., 28 (1989), pp. 1787-1801] and some new ones introduced in this paper. For the deflection and rotatio n we give error estimates which are optimal with respect to the mesh s ize h and optimal up to O(k(epsilon)), epsilon > 0 arbitrary, with res pect to the polynomial degree k. We also obtain estimates for the erro r in the shear force, calculated via two different methods. Our analys is utilizes some recent results of ours for the mixed method for the S tokes problem, as well as hp interpolation estimates for mixed methods for second-order elliptic equations. In this regard, we derive new hp results in this paper for the Breazi-Douglas-Fortin-Marini spaces and improve upon previous estimates for the Brezzi-Douglas-Marini spaces.