  Recently, the authors have proposed and analyzed isogeometric tearing and
interconnecting (IETI-DP) solvers for multi-patch discretizations in
Isogeometric Analysis. Conforming and discontinuous Galerkin settings have been
considered. In both cases, we have assumed that the interfaces between the
patches consist of whole edges. In this paper, we present a generalization that
allows us to drop this requirement. This means that the patches can meet in
T-junctions, which increases the flexibility of the geometric model
significantly. We use vertex-based primal degrees of freedom. For the
T-junctions, we propose to follow the idea of "fat vertices".
