LOCKING-FREE REISSNERMINDLIN ELEMENTS WITHOUT REDUCED INTEGRATION Summary: LOCKING-FREE REISSNER­MINDLIN ELEMENTS WITHOUT REDUCED INTEGRATION DOUGLAS N. ARNOLD, FRANCO BREZZI, RICHARD S. FALK, AND L. DONATELLA MARINI Abstract. In a recent paper of Arnold, Brezzi, and Marini [4], the ideas of discontinuous Galerkin methods were used to obtain and analyze two new families of locking free finite element methods for the approximation of the Reissner­Mindlin plate problem. By follow- ing their basic approach, but making different choices of finite element spaces, we develop and analyze other families of locking free finite elements that eliminate the need for the introduction of a reduction operator, which has been a central feature of many locking-free methods. For k 2, all the methods use piecewise polynomials of degree k to approximate the transverse displacement and (possibly subsets) of piecewise polynomials of degree k - 1 to approximate both the rotation and shear stress vectors. The approximation spaces for the rotation and the shear stress are always identical. The methods vary in the amount of interelement continuity required. In terms of smallest number of degrees of freedom, the simplest method approximates the transverse displacement with continuous, piecewise quadratics and both the rotation and shear stress with rotated linear Brezzi-Douglas-Marini elements. 1. Introduction In the Reissner­Mindlin model of a clamped plate, one seeks to determine the rotation vector and the transverse displacement w which minimize over H1 Collections: Engineering; Mathematics