1. Introduction

The residual error estimator was developed in 1993 by Bernardi-Métivet-Verfurth [bib1]. It is an explicit error estimator involving the residuals of equilibrium equations (hence its name). It applies to elliptical problems (Poisson, Stokes, or linear elasticity) in 2 or 3 dimensions. These problems are supposed to be discretized by finite elements associated with regular triangulation.

Historically, the first explicit error estimator for balance faults was due to Babuska and Rheinbolt [bib2] for 1D problems with linear elements. Gago extended this estimator to 2D and added traction jumps at the interfaces of the [bib3] and [bib4] elements to the formulas. New estimators were then proposed, in which surface tension defects at the boundaries of the field were also taken into account as well as an improvement in the estimation of inter-element jumps giving more reliable results.

Here we are interested in the residue estimator applied to the case of linear elasticity. The aim is, at the end of an elastic calculation, to determine the error map on the mesh in order to possibly adapt this one (by refinement and/or deraffination) or simply for information. The adaptation can be done by chaining with the Homard slicing software.