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In the Isogeometric Analysis (IGA) framework, the computational domain hasvery often a multipatch representation. The multipatch domain can be obtainedby a volume segmentation of a boundary represented domain, e.g., provided by aComputer Aided Design (CAD) model. Typically, small gap and overlapping regionscan appear at the patch interfaces of such multipatch representations. In thecurrent work we consider multipatch representations having only smalloverlapping regions between the patches.  We develop a Discontinuous Galerkin (DG)- IGA method which can be immediatelyapplied to these representations. Our method appropriately connects the fluxesof the one face of the overlapping region with the flux of the opposite face.We provide a theoretical justification of our approach by splitting the wholeerror into two components: the first is related to the incorrect representationof the patches (consistency error) and the second to the approximationproperties of the IGA space. We show bounds for both components of the error.We verify the theoretical error estimates in a series of numerical examples.

Discontinuous Galerkin Isogeometric Analysis for segmentations generating overlapping regions