Analysis of discontinuous Galerkin dual-primal isogeometric tearing and interconnecting methods

In this paper, we present the analysis of the discontinuous Galerkin dual-primal isogeometric tearing and interconnecting method (dG-IETI-DP) for a multipatch discretization in two-space dimensions where we only consider vertex primal variables. As model problem, we use the Poisson equation with globally constant diffusion coefficient. The dG-IETI-DP method is a combination of the dual-primal isogeometric tearing and interconnecting method (IETI-DP) with the discontinuous Galerkin (dG) method. We use the dG method only on the interfaces to couple different patches. This enables us to handle non-matching grids on patch interfaces as well as segmentation crimes (gaps and overlaps) between the patches. The purpose of this paper is to derive quasi-optimal bounds for the condition number of the preconditioned system with respect to the maximal ratio H/h := max(k)(H-k/h(k)) of subdomain diameter and mesh size. Moreover, we show that the condition number is independent of the number of patches, but depends on the mesh sizes of neighboring patches h(l)/h(k) and the parameter delta in the dG penalty term.