| A new finite element method for the solution of the general magnetostatic problem is formulated and analyzed. The space of trial functions consists of solenoidal piecewise polynomial vector-functions. We start with an integral formulation, for the flux density, in the domain occupied by magnetic material. Using the properties of the spectrum of the relevant singular integral operator we derive a weak formulation with an integral operator on the boundary only. Thus the resulting finite element matrix is sparse. Using the method of monotone operators, existence and uniqueness of solution are proved. Error estimates are derived with the special emphasis on the case when magnetic permeability is large. Finally, numerical solution of the problem by successive iteration is analyzed. |
