  This article deals with the computation of guaranteed lower bounds of the
error in the framework of finite element (FE) and domain decomposition (DD)
methods. In addition to a fully parallel computation, the proposed lower bounds
separate the algebraic error (due to the use of a DD iterative solver) from the
discretization error (due to the FE), which enables the steering of the
iterative solver by the discretization error. These lower bounds are also used
to improve the goal-oriented error estimation in a substructured context.
Assessments on 2D static linear mechanic problems illustrate the relevance of
the separation of sources of error and the lower bounds' independence from the
substructuring. We also steer the iterative solver by an objective of precision
on a quantity of interest. This strategy consists in a sequence of solvings and
takes advantage of adaptive remeshing and recycling of search directions.
