 
Summary: A ROTATED NONCONFORMING RECTANGULAR MIXED
ELEMENT FOR ELASTICITY
GERARD AWANOU
Abstract. We present in this paper a low order nonconforming mixed element
for plane elasticity on rectangular meshes. The 3 dimensional space of rigid body
motions is used to approximate the displacement and a 16 dimensional space is used
to discretize the space of symmetric tensors. This element may be viewed as the
rectangular analogue of the nonconforming ArnoldWinther element and is related
to a discrete version of the elasticity differential complex with a nonconforming H2
element related to the rotated Q1 element.
1. Introduction
It is well known that it is extremely difficult to construct mixed finite elements for elas
ticity in stress displacement formulation. In a pioneering work, Arnold and Winther
constructed the first mixed elements for plane elasticity with symmetric stress fields,
using polynomial shape functions, [2].
Previous works circumvent the difficulty of the symmetry condition by using com
posite elements, weakening or abandoning the symmetry condition, cf. [2] and the
references therein. As explained in [2], vertex degrees of freedom are unavoidable
for a finite element space for the stress field with continuous symmetric matrix fields
if one imposes interelement continuity only by means of quantities defined on the
