Recovery-based a posteriori error analysis for plate bending problems

TL;DR

This paper introduces two novel recovery-based a posteriori error estimators for the Hellan--Herrmann--Johnson method in Kirchhoff--Love plate theory, validated through numerical experiments.

Contribution

It proposes new error estimators that improve error control in plate bending problems, combining postprocessed fields and superconvergence techniques.

Findings

Effective error estimation demonstrated in numerical tests

Controls both deflection and moment errors

Validates theoretical results with experiments

Abstract

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 superconvergent postprocessed moment field and deflection. The effectiveness of the theoretical results is numerically validated in several experiments.