  This paper presents a strategy for a posteriori error estimation for
substructured problems solved by non-overlapping domain decomposition methods.
We focus on global estimates of the discretization error obtained through the
error in constitutive relation for linear mechanical problems. Our method
allows to compute error estimate in a fully parallel way for both primal (BDD)
and dual (FETI) approaches of non-overlapping domain decomposition whatever the
state (converged or not) of the associated iterative solver. Results obtained
on an academic problem show that the strategy we propose is efficient in the
sense that correct estimation is obtained with fully parallel computations;
they also indicate that the estimation of the discretization error reaches
sufficient precision in very few iterations of the domain decomposition solver,
which enables to consider highly effective adaptive computational strategies.
