1. Introduction

Research into error estimators on solutions obtained by finite element calculations and their coupling with adaptive mesh procedures has grown considerably in recent years. The aim is to overcome the possible inadequacy of a modeling by automatically adapting the mesh to the solution sought according to certain criteria (equidistribution of the discretization error, minimization of the number of nodes to achieve a given precision, lower cost).

A posteriori type error estimator is presented here in the context of linear and homogeneous elasticity. Historically, this estimator, proposed by ZHU - ZIENKIEWICZ [bib1] in 1987, was widely used because of its ease of implementation in existing calculation codes and its low cost. Nevertheless, the poor reliability of this estimator for elements of even degree was observed empirically (underestimation of the error) and led the authors to modify their method in 1992 [bib2], [bib3] with numerical verification of the asymptotic convergence of the estimator on all types of elements.

However, as the field of application of the 1992 version is currently smaller (see [3.2]), the two versions of this estimator have been implemented in*Aster* and are the subject of this note.