Finite element verification in the case of missing data

The objective of this work is to obtain an a posteriori estimate of the discretization error of a reference problem which, in our case, is a linear elasticity problem solved using the finite element method. Classically, one assumes that both the reference problem and its discretized solution are known. The originality of the present work is that some of the boundary conditions are considered to be missing or incomplete to assess the error. The proposed method is particularly suited to industrial situations where only the finite element solution is available. We present and illustrate two possible strategies. The error estimator used is the error in constitutive relation.