  This paper investigates the question of the building of admissible stress
field in a substructured context. More precisely we analyze the special role
played by multiple points. This study leads to (1) an improved recovery of the
stress field, (2) an opportunity to minimize the estimator in the case of
heterogeneous structures (in the parallel and sequential case), (3) a procedure
to build admissible fields for FETI-DP and BDDC methods leading to an error
bound which separates the contributions of the solver and of the
discretization.
