Analysis of some low-order finite element schemes for Mindlin-Reissner and Kirchhoff plates

Summary We set up a framework for analyzing mixed finite element methods for the plate problem using a mesh dependent energy norm which applies both to the Kirchhoff and to the Mindlin-Reissner formulation of the problem. The analysis techniques are applied to some low order finite element schemes where three degrees of freedom are associated to each vertex of a triangulation of the domain. The schemes proceed from the Mindlin-Reissner formulation with modified shear energy.Dedicated to Professor Ivo Babuka on the occasion of his 60th birthday