Bracco, CesareGiannelli, CarlottaKapl, MarioVázquez, Rafael2020-10-262020-10-262020-10-262020-12-0110.1016/j.camwa.2020.03.018https://infoscience.epfl.ch/handle/20.500.14299/172761Adaptive isogeometric methods for the solution of partial diifferential 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.text::journal::journal article::research article