Adaptive subdivision integration over overlapping curvilinear elements with application to bonded contact on non-conformal meshes

Reliable integration over intersections of independently generated curved finite-element meshes is essential for conservative transfer and non-conformal coupling, yet these intersections are difficult to represent explicitly. This study formulates and systematically evaluates adaptive subdivision integration, which computes intersection measures directly from the isoparametric maps without constructing a separate intersection mesh. The method covers curved planar and spatial element intersections as well as embedded surface portions. Comparisons with analytical measures and separately sampled numerical estimates demonstrate accurate results for all considered element families, while adaptive refinement concentrates the computational work near intersection boundaries. The method is then incorporated into a bonded-coupling formulation for non-conformal meshes with local gaps and overlaps. Evaluating paired interface contributions on the same geometric partition preserves their discrete transpose relation. The results establish adaptive subdivision integration as an effective tool for non-conformal engineering analysis.