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

Abstract

In this paper, we develop a discontinuous Galerkin Isogeometric Analysis method for solving elliptic problems on decompositions of the computational domain into volumetric patches 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 the dG-norm, with respect to the mesh size and the gap distance. Numerical examples, performed for two-, three- and even four-dimensional computational domains, demonstrate the robustness of the proposed numerical method and validate the estimates predicted by the theory.