  We propose a new discontinuous Galerkin Isogeometric Analysis (IgA) technique
for the numerical solution of elliptic diffusion problems in computational
domains decomposed into volumetric patches with non-matching interfaces. Due to
an incorrect segmentation procedure, it may happen that the interfaces of
adjacent subdomains don't coincide. In this way, gap regions, which are not
present in the original physical domain, are created. In this paper, the gap
region is considered as a subdomain of the decomposition of the computational
domain and the gap boundary is taken as an interface between the gap and the
subdomains. We apply a multi-patch approach and derive a subdomain variational
formulation which includes interface continuity conditions and is consistent
with the original variational formulation of the problem. The last formulation
is further modified by deriving interface conditions without the presence of
the solution in the gap. Finally, the solution of this modified problem is
approximated by a special discontinuous Galerkin IgA technique. The ideas are
illustrated on a model diffusion problem with discontinuous diffusion
coefficients. We develop a rigorous theoretical framework for the proposed
method clarifying the influence of the gap size onto the convergence rate of
the method. The theoretical estimates are supported by numerical examples in
two- and three-dimensional computational domains.
