Postprocessing and a posteriori error analysis for plate bending problems

We present two new a posteriori error estimates for the Hellan--Herrmann--Johnson method in Kirchhoff--Love plate theory. The first error estimator uses a postprocessed deflection and controls the $L^2$ moment error and the discrete $H^2$ deflection error. The second one is based on the postprocessed deflection and moment fields and superconvergence analysis in both variables. The effectiveness of the theoretical results is numerically validated in several experiments.