  In this work, we study the approximation properties of multi-patch dG-IgA
methods, that apply the multipatch Isogeometric Analysis (IgA) discretization
concept and the discontinuous Galerkin (dG) technique on the interfaces between
the patches, for solving linear diffusion problems with diffusion coefficients
that may be discontinuous across the patch interfaces. The computational domain
is divided into non-overlapping sub-domains, called patches in IgA, where
$B$-splines, or NURBS finite dimensional approximations spaces are constructed.
The solution of the problem is approximated in every sub-domain without
imposing any matching grid conditions and without any continuity requirements
for the discrete solution across the interfaces. Numerical fluxes with interior
penalty jump terms are applied in order to treat the discontinuities of the
discrete solution on the interfaces. We provide a rigorous a priori
discretization error analysis for problems set in 2d- and 3d- dimensional
domains, with solutions belonging to $W^{l,p}, l\geq 2,{\ } p\in
({2d}/{(d+2(l-1))},2]$. In any case, we show optimal convergence rates of the
discretization with respect to the dG - norm.
