Taylor--Hood Discretization of the Reissner--Mindlin Plate

A shear-locking free finite element discretization of the Reissner--Mindlin plate model is introduced. The rotation is discretized with piecewise polynomials of degree $k+2$ while the degree k≥0 is used for the displacement gradient. The method is closely related to the (generalized) Taylor--Hood pairing. In this case the general theory of saddle-point problems with penalty cannot exclude that the convergence speed for the rotation is limited by the lower rate expected for the displacement. However, in this paper, it is shown that the rotations are approximated at optimal order of accuracy. This superconvergence phenomenon is proved by means of the approximation properties of the Fortin operator for the Taylor--Hood element and the Galerkin projection.