Rectangular mixed elements for elasticity with weakly imposed symmetry condition

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.