New advances on a posteriori error on constitutive relation in f.e. analysis Original Research Article

This paper deals with error estimators based on residuals on the constitutive relation which have been developed for the past 20 years at Cachan. Especially in the case of elasticity, these error estimators can become poor in situations where the material and the mesh are strongly anisotropic. The crucial point herein is the construction of equilibrated stress fields from the computed finite element solution. Therefore, in this paper, the approach and in particular this last point are re-examined. Several important modifications are introduced in the concepts and basic techniques. Hence, a new generation of error estimators which seem to be extremely robust upon initial applications has been generated.