  Nowadays, a posteriori error control methods have formed a new important part
of the numerical analysis. Their purpose is to obtain computable error
estimates in various norms and error indicators that show distributions of
global and local errors of a particular numerical solution.
  In this paper, we focus on a particular class of domain decomposition methods
(DDM), which are among the most efficient numerical methods for solving PDEs.
We adapt functional type a posteriori error estimates and construct a special
form of error majorant which allows efficient error control of approximations
computed via these DDM by performing only subdomain-wise computations. The
presented guaranteed error bounds use an extended set of admissible fluxes
which arise naturally in DDM.
