Weakly over-penalized discontinuous Galerkin schemes for Reissner–Mindlin plates without the shear variable

This paper introduces a new locking–free formulation that combines the discontinuous Galerkin methods with weakly over-penalized techniques for Reissner–Mindlin plates. We derive optimal a priori error estimates in both the energy norm and $$L^2$$L2 norm for polynomials of degree $$k=2$$k=2, and we extend the results concerning the energy norm to higher-order polynomial degrees. Numerical tests confirm our theoretical predictions.

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