Thin-layer formulation for non-conforming interfaces in FEM

Abstract

Thin interfaces such as coatings, adhesive films, and thermal contact regions can strongly influence heat transfer and structural response, but are costly to resolve with standard finite elements. This work introduces a unified thin-layer interface formulation on non-conforming interfaces, where the thin layer is collapsed into effective interface parameters. A central contribution is to show that, once posed on a non-conforming interface, the thin-layer formulation naturally yields Nitsche-type coupling terms, thereby establishing a previously unreported bridge between thin-layer interface models and Nitsche-type non-conforming coupling. The generic formulation is presented for both scalar- and vector-valued cases: steady heat conduction and linear elasticity. Two representative examples demonstrate that the interface model reproduces the response of explicitly meshed thin layers while retaining the geometric flexibility of non-conforming meshes.