A New Family of Mixed Methods for the Reissner-Mindlin Plate Model Based on a System of First-Order Equations

The mixed method for the biharmonic problem introduced in (Behrens and Guzman, SIAM J. Numer. Anal., 2010) is extended to the Reissner-Mindlin plate model. The Reissner-Mindlin problem is written as a system of first order equations and all the resulting variables are approximated. However, the hybrid form of the method allows one to eliminate all the variables and have a final system only involving the Lagrange multipliers that approximate the transverse displacement and rotation at the edges of the triangulation. Mixed finite element spaces for elasticity with weakly imposed symmetry are used to approximate the bending moment matrix. Optimal estimates independent of the plate thickness are proved for the transverse displacement, rotations and bending moments. A post-processing technique is provided for the displacement and rotations variables and we show numerically that they converge faster than the original approximations.