Robust equilibrated a posteriori error estimators for the Reissner-Mindlin system

TL;DR

This paper introduces a new robust a posteriori error estimator for the Reissner-Mindlin system using conforming finite elements and equilibrated fluxes, with proven reliability and efficiency through numerical tests.

Contribution

It presents a novel a posteriori error estimator that provides reliable upper bounds with near-optimal constants for the Reissner-Mindlin system.

Findings

Estimator provides an upper bound with constant close to one.

Lower bounds depend on mesh shape regularity.

Numerical tests confirm reliability and efficiency.

Abstract

We consider a conforming finite element approximation of the Reissner-Mindlin system. We propose a new robust a posteriori error estimator based on H(div) conforming finite elements and equilibrated fluxes. It is shown that this estimator gives rise to an upper bound where the constant is one up to higher order terms. Lower bounds can also be established with constants depending on the shape regularity of the mesh. The reliability and efficiency of the proposed estimator are confirmed by some numerical tests.