Isogeometric analysis with C1 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 C0 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 C1 continuity on two or more patches. In this paper, we show how these approaches can be combined with the hierarchical construction to obtain global C1 continuous hierarchical splines on two-patch domains. A selection of numerical examples is presented to highlight the features and effectivity of the construction.