Discontinuous Galerkin Isogeometric Analysis of elliptic problems on segmentations with non-matching interfaces

In the Isogeometric Analysis framework for treating realistic problems, it is usually necessary to decompose the domain into volumetric subdomains (patches). At the end of the procedure for constructing suitable parametrization mappings for the subdomains, the control points related to interfaces may not appropriately match resulting in non-matching parametrized interfaces. In this case, gap regions can appear between the subdomains, which do not exist in the case of matching interface parametrizations. In this paper a discontinuous Galerkin Isogeometric Analysis method is developed for solving elliptic problems on decompositions with non-matching parametrized interfaces. We specially focus on high order numerical solutions for complex gap regions and extend ideas from our previous work on simple gap regions. For the communication of the numerical solution between the subdomains, which are separated by the gap region, discontinuous Galerkin numerical fluxes are constructed taking into account the diametrically opposite points on the boundary of the gap. Due to lack of information on the behavior of the solution in the gap region, the fluxes coming from the interior of the gap are approximated by Taylor expansions with respect to the adjacent subdomain solutions. We follow the same ideas of our previous work and show a priori error estimates in dG-norm, with respect to the mesh size and the gap distance, which quantifies the maximum distance between two diametrically opposite points on the gap boundary. Numerical examples performed in twoand three-dimensional computational domains demonstrate the robustness of the proposed numerical method and validate the theoretical predicted estimates.