[en] The aim of this work is investigation of possibilities of using high-order harmonic basis for solving some magnetostatic problems. We consider known methods with our basis and the approach earlier elaborated by the authors. We present numerical results of their comparison when solving a linear problem on sequences of meshes with various parameters h and p. For a nonlinear problem with respect to two scalar potentials, it is shown that this model, in the suggested new weak formulation, keeps the property of monotonicity. From the results of this work it may be concluded that the harmonic basis gives more exact approximations on adaptive meshes for the considered magnetostatic problems in comparison with the usual approach.