  This work presents a numerical study of functional type a posteriori error
estimates for IgA approximation schemes in the context of elliptic
boundary-value problems. Along with the detailed discussion of the most crucial
properties of such estimates, we present the algorithm of a reliable solution
approximation together with the scheme of efficient a posteriori error bound
generation-based on solving an auxiliary problem with respect to an introduced
vector-valued variable. In this approach, we take advantage of B-(THB-)spline's
high smoothness for the auxiliary vector function reconstruction, which, at the
same time, allows to use much coarser meshes and decrease the number of
unknowns substantially. The most representative numerical results, obtained
during a systematic testing of error estimates, are presented in the second
part of the paper. The efficiency of the obtained error bounds is analysed from
both the error estimation (indication) and the computational expenses points of
view. Several examples illustrate that functional error estimates
(alternatively referred to as the majorants and minorants of deviation from an
exact solution) perform a much sharper error control than, for instance,
residual-based error estimates. Simultaneously, assembling and solving the
routines for an auxiliary variable reconstruction which generate the majorant
of an error can be executed several times faster than the routines for a primal
unknown.
