Discontinuous Galerkin with Weakly Over-Penalized Techniques for Reissner–Mindlin Plates

In this article we introduce a new locking-free completely discontinuous formulation for Reissner–Mindlin plates that combines the discontinuous Galerkin methods with weakly over-penalized techniques. We establish a new discrete version of Helmholtz decomposition and some important residual estimates. Combining the residual estimates with enriching operators we derive an optimal a priori error estimate in the energy norm. We obtain robust a posteriori error estimators and prove their reliability and efficiency.