Rectangular mixed elements for elasticity with weakly imposed symmetry condition

Abstract

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.