FEM and BEM coupling in elastostatics using localized Lagrange multipliers

The equations produced by the finite and boundary element methods in structural mechanics are expressed in different variables and cannot be linked without modifications. Conventional coupling methods of these numerical techniques have traditionally been based on the use of classical Lagrange multipliers making a direct connection of the two solids through their common interfaces using matching meshes and altering the formulation of one of the methods to make it compatible with the other. In this work, a discrete surface called frame is interposed between the connected subdomains to approximate their common interface displacements, it is treated using a finite element discretization and connected to each substructure using localized Lagrange multipliers collocated at the interface nodes. This methodology facilitates the connection of non‐matching finite and boundary element meshes avoiding modifications to the numerical methods used and providing a partitioned formulation, which preserves software modularity.