This work presents an innovative approach to tackle the challenge of implementing general non-conforming weak Cn-continuous domain couplings in isogeometric analysis. Building on the established mortar method, the approach extends it by introducing additional constraints on derivatives up to a specified order. The study comprehensively elucidates the method within an abstract variational framework, covering aspects such as discretisation in isogeometric analysis, dual space selection, efficient handling of crosspoints and wirebaskets, and the evaluation of mortar integrals. Special attention is given to constructing isogeometric approximation spaces that inherently satisfy higher-order coupling conditions. The performance and applicability of the method are explored in diverse engineering problems, including elasticity, heat conduction, diffusion, and Phase-Field-Crystal modelling. Through a series of simulations, the study demonstrates the efficiency and applicability of the approach in various technical domains.weiterlesen