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The application of the equivalent source methods for the numerical calculation of the total magnetic force acting upon a permanent magnet is proposed. These methods are formulated in terms of the external field, which allows the complete avoidance of the numerical inaccuracies affecting force computation due to the singularity of the self‐field of the magnet on its edges. It is shown, with the help of some 2D and 3D test cases, that the proposed formulae provide reliable and stable results, even when the FEM mesh is not refined. Such results have also been compared with those derived from more traditional methods, such as the surface integration of the Maxwell’s stress tensor and the virtual work method, exhibiting better precision and lower computational costs.

This paper presents new developments relevant to error estimate and mesh adaptioin procedures based on the "Local Field Error" approach for linear and non-linear magnetostatic problems in 2D. Tihe error problem is solved "locally" on each element of the mesh under analysis using an "edge element" description. Boulndary conditions for local problems are derived from the jump in the normal derivatives of the vector potential at inter-element boundaries and from physical constraints on the field. The procedure has been succesfully tested, even in problems of industrial complexity; some of the obtained results are presented and discussed.

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