Jimenez Recio, PabloPabloJimenez RecioSchweitzer, Marc AlexanderMarc AlexanderSchweitzer2024-09-022024-09-022024https://publica.fraunhofer.de/handle/publica/47434710.1016/j.cma.2024.1170022-s2.0-85190989560In this paper we develop a partition-of-unity construction of the stabilization function required in Nitsche's method, which can be seen as a generalization of the element-wise construction that is widely used in finite element methods. This allows for the use of Nitsche's method within the Partition of Unity Method with a stabilization function that is not simply a constant over the whole boundary. In addition to that, we introduce a patch-aggregation approach designed to avoid arbitrarily large values of the stabilization function and the associated ill-conditioned systems and deteriorated convergence rates. We present numerical results to validate the proposed methods, covering Dirichlet boundary conditions, interface constraints and higher-order problems. These results clearly show that our approach leads to optimal convergence rates.enopen accessEssential boundary conditionsMeshfree methodNitsche's methodPartition of unity methodjournal article