Analysis of some stabilized low-order mixed finite element methods for Reissner–Mindlin plates Original Research Article

New low-order mixed finite element methods are established for the Reissner–Mindlin plate problem under a clamped boundary condition, employing equal order (bi)linear interpolants for the rotation and the lateral displacement and discontinuous constant (or constant locally enriched by a special function, or linear) interpolant for the shear stress, where two stabilization terms are introduced one of which is used to control the jump of the normal trace of the shear stress across the interelement boundaries and the other is in essence used to control the rotation by modifying the thickness of the plate. When using macro-element for the displacement, the stabilization term pertaining to the jump of the normal trace of the shear stress can be dropped, since the jump can be automatically controlled. It is shown that all these methods are stable and optimal convergent, including in the L2-norm for the rotation and the displacement, uniform in the thickness of the plate.