New advances on a posteriori error on constitutive relation in f. e. analysis. (English) Zbl 0906.73064

Summary: 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.


74S05 Finite element methods applied to problems in solid mechanics
74A20 Theory of constitutive functions in solid mechanics
65N15 Error bounds for boundary value problems involving PDEs
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