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This paper discusses the application of Lagrange multipliers to restore field continuity across nonconforming surfaces in 3-D problems. The method makes it in particular possible to implement the relative motion of stator and rotor without remeshing in the 3-D Finite Element (FE) modeling of electrical machines. The choice of a special set of biorthogonal shape functions for the Lagrange multiplier makes it possible to preserve the positive definiteness of the FE system. It is shown that such a biorthogonal basis cannot be constructed canonically for a 3-D magnetic vector potential formulation. For a 3-D magnetic scalar potential formulation, however, the situation is different and a biorthogonal basis can be found.