It is very common practice to use the vector potential as an unknown variable in the finite element method (F. E. M.) for magnetic field analyses, and then its differentiation is necessarily performed to obtain magnetic flux density. Thus, for obtaining accurate magnetic flux density, the analytical region must be divided into dense elements at the expense of large memory and tremendous computation time. In order to overcome this problem, the authors have developed a novel F. E. M. by using magnetic flux density directly as an unknown variable. There has been, however, no paper discussing the difference of accuracy among those methods used vector potential or magnetic flux density as the unknown variable and used the first or second order elements. In this paper, the formulation of the novel F. E. M. is developed for two-dimensional and axi-symmetrical field problems based on the second order finite element, and the usefulness of the novel F. E. M. is described by comparing error assessment of the magnetic flux density with the traditional methods. To illustrate the capability of the novel F. E. M., some examples of the practical models are demonstrated.

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