  The Isogeometric Analysis (IgA) of boundary value problems in complex domains
often requires a decomposition of the computational domain into patches such
that each of which can be parametrized by the so-called geometrical mapping. In
this paper, we develop discontinuous Galerkin (dG) IgA techniques for solving
elliptic diffusion problems on decompositions that can include non-matching
parametrizations of the interfaces, i.e., the interfaces of the adjacent
patches may be not identical. The lack of the exact parametrization of the
patches leads to the creation of gap and overlapping regions between the
patches. This does not allow the immediate use of the classical numerical
fluxes that are known in the literature. The unknown normal fluxes of the
solution on the non-matching interfaces are approximated by Taylor expansions
using the values of the solution computed on the boundary of the patches These
approximations are used in order to build up the numerical fluxes of the final
dG IgA scheme and to couple the local patch-wise discrete problems. The
resulting linear systems are solved by using efficient domainecomposition
methods based on the tearing and interconnecting technology. We present
numerical results of a series of test problems that validate the theoretical
estimates presented.

Numerical Analysis