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A method for coupling magnetostatic and magnetodynamic finite element formulations with lumped reluctances is developed. Two dual h and b-conform formulations are extended to define the necessary magnetic relations between the magnetic fluxes and the magnetomotive forces. Adequate surface scalar potentials are defined and adequate boundary terms in the weak formulations are used. The magnetic relations can then be included in a reluctance network, in which the coupling of finite element regions and lumped regions aims at higher computational efficiency. The methods are developed in three dimensions, using a coupling of nodal and edge finite element approximations for the unknowns, and can easily be particularized in two dimensions.