Towards a IETI-DP solver on non-matching multi-patch domains

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".