  This work is concerned with a posteriori error estimates of the functional
type for approximations constructed by space-time IgA scheme presented in paper
by Langer, Neumueller, and Moore (2016). We consider approxima- tions in the
corresponding IgA spaces based on elliptic and bounded bilinear form
(associated with the spatial part). It is proved that the approximations
satisfy classic a priori error estimates. Also, we deduce a posteriori error
estimates for a stabilized weak formulation of the considered parabolic initial
boundary value problem (I-BVP). They are derived by a general functional method
and do not contain mesh dependent constants. The estimates are valid for a wide
class of approximations. In particular, they imply estimates for the discrete
norm of IgA approximations. Moreover, we introduce different forms of a
posteriori error estimates (error majorants) and establish equivalence of
majorants and energy error norm. This property justifies efficiency and
reliability of a posteriori error estimates. Another important property of the
estimates is their flexibility with respect to a certain amount of free
parameters. Using these parameters we can obtain estimates for different error
norms and minimize the respective majorant in order to find the best possible
bound of the error.
