Isogeometric analysis with C^1 hierarchical functions on planar two-patch geometries

Adaptive isogeometric methods for the solution of partial differential equations rely on the construction of locally refinable spline spaces. A simple and efficient way to obtain these spaces is to apply the multi-level construction of hierarchical splines, that can be used on single-patch domains or in multi-patch domains with C-0 continuity across the patch interfaces. Due to the benefits of higher continuity in isogeometric methods, recent works investigated the construction of spline spaces with global C-1 continuity on two or more patches. In this paper, we show how these approaches can be combined with the hierarchical construction to obtain global C-1 continuous hierarchical splines on two-patch domains. A selection of numerical examples is presented to highlight the features and effectivity of the construction.