Purpose: The purpose of this paper is to develop a sub-domain perturbation technique for refining magnetic circuit models with finite element (FE) models of different dimensions. Design/methodology/approach – A simplified problem considering ideal flux tubes is first solved, as either a 1D magnetic circuit or a simplified FE problem. Its solution is then corrected via FE perturbation problems considering the actual flux tube geometry and the exterior regions, that allow first 2D and then 3D leakage fluxes. Each of these sub-problems requires an appropriate proper volume mesh, with no need of interconnection. The solutions are transferred from one problem to the other through projections of source fields between meshes. Findings: The developed perturbation FE method allows to split magnetic circuit analyses into subproblems of lower complexity with regard to meshing operations and computational aspects. A natural progression from simple to more elaborate models, from 1D to 3D geometries, is thus possible, while quantifying the gain given by each model refinement and justifying its utility. Originality/value: Approximate problems with ideal flux tubes are accurately corrected when accounting for leakage fluxes via surface sources of perturbations. The constraints involved in the subproblems are carefully defined in the resulting FE formulations, respecting their inherent strong and weak nature. As a result, an efficient and accurate computation of local fields and global quantities, i.e. flux, MMF, reluctance, is obtained. The method is naturally adapted to parameterized analyses on geometrical and material data.