  We present new rectangular mixed finite elements for linear elasticity. The
approach is based on a modification of the Hellinger-Reissner functional in
which the symmetry of the stress field is enforced weakly through the
introduction of a Lagrange multiplier. The elements are analogues of the lowest
order elements described in Arnold, Falk and Winther [ Mixed finite element
methods for linear elasticity with weakly imposed symmetry. Mathematics of
Computation 76 (2007), pp. 1699--1723]. Piecewise constants are used to
approximate the displacement and the rotation. The first order BDM elements are
used to approximate each row of the stress field.

Numerical Analysis