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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 et al. (Math Comput 76:1699---1723, 2007). 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.

Rectangular mixed elements for elasticity with weakly imposed symmetry condition