On the uniqueness of solution of magnetostatic vector-potential problems by three-dimensional finite-element methods

Abstract

Force calculations with three-dimensional scalar potential based finite-element programs (abstract) J. Appl. Phys. 67, 5833 (1990) In this paper, particular attention is paid to the impact of finite-element approximation on uniqueness and to approximations implicit in finite element formulations from the uniqueness requirements standpoint. It is also shown that the flux density is unique without qualifications. The theoretical and numerical uniqueness of the magnetic vector potential in three-dimensional problems is also given. This analysis is restricted to linear, isotropic media with Dirichlet Boundary conditions. As an interesting consequence of this analysis it is shown that, under usual conditions adopted in obtaining three-dimensional finite-element solutions, it is not necessary to specify div A in order that A be uniquely defined.