Local estimation of the error in the von Mises' stress and L2-norm of the stress for linear elasticity problems

Purpose - This paper aims to focus on the local quality of outputs of interest computed by a finite element analysis in linear elasticity. Design/methodology/approach - In particular outputs of interest are studied which do not depend linearly on the solution of the problem considered such as the L2-norm. of the stress and the von Mises' stress. The method is based on the concept of error in the constitutive relation. Findings - The method is illustrated through 2D test examples and shows that the proposed error estimator leads in practice to upper bounds of the output of interest being studied. Practical implications - This tool is directly usable in the design stage. It can be used to develop efficient adaptive techniques. Originality/value - The interest of this paper is to provide an estimation of the local quality of L2-norm of the stress and the Von Mises' stress as well as practical upper bounds for these quantities.