Recovery-based a posteriori error analysis for plate bending problems

We present two new recovery-based 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 controls the $L^2\times H^1$ total error and utilizes the postprocessed moment field and deflection and superconvergence analysis in both variables. The effectiveness of the theoretical results is numerically validated in several experiments.