Crosspoint modification for multi-patch isogeometric analysis

A crosspoint modification for general Cⁿ continuous mortar coupling conditions is presented. In particular, we modify the extended mortar method as introduced in Schuß et al. (2019) and Dittmann et al. (2019) to deal with crosspoints as they arise in multi-patch geometries. This modification is constructed in such a way, that we decouple the Lagrange multipliers at the crosspoint to avoid a global coupling condition across all interfaces. Moreover, we recast the underlying B-Splines such that they preserve the higher order best approximation property across the interface and the crosspoint. A detailed investigation is presented in the context of second order thermal problems, fourth order Cahn–Hilliard and sixth order Swift–Hohenberg formulations.