 
Summary: LOCKINGFREE 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 lockingfree
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 BrezziDouglasMarini
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
