  In this paper, we develop a convergence theory for Dual-Primal Isogeometric
Tearing and Interconnecting (IETI-DP) solvers for isogeometric multi-patch
discretizations of the Poisson problem, where the patches are coupled using
discontinuous Galerkin. The presented theory provides condition number bounds
that are explicit in the grid sizes h and in the spline degrees p. We give an
analysis that holds for various choices for the primal degrees of freedom:
vertex values, edge averages, and a combination of both. If only the vertex
values or both vertex values and edge averages are taken as primal degrees of
freedom, the condition number bound is the same as for the conforming case. If
only the edge averages are taken, both the convergence theory and the
experiments show that the condition number of the preconditioned system grows
with the ratio of the grid sizes on neighboring patches.
