  The problem of developing an adaptive isogeometric method (AIGM) for solving
elliptic second-order partial differential equations with truncated
hierarchical B-splines of arbitrary degree and different order of continuity is
addressed. The adaptivity analysis holds in any space dimensions. We consider a
simple residual-type error estimator for which we provide a posteriori upper
and lower bound in terms of local error indicators, taking also into account
the critical role of oscillations as in a standard adaptive finite element
setting. The error estimates are properly combined with a simple marking
strategy to define a sequence of admissible locally refined meshes and
corresponding approximate solutions. The design of a refine module that
preserves the admissibility of the hierarchical mesh configuration between two
consectutive steps of the adaptive loop is presented. The contraction property
of the quasi-error, given by the sum of the energy error and the scaled error
estimator, leads to the convergence proof of the AIGM.
