The paper is concerned with stability and accuracy of n-order finite element (FE) steady-state solutions of traveling magnetic field problem. It is found that the odd-order FE solutions (nis the odd number) are stable0 < sigma|u|h|nu < f(n) simeq 2.0 + 1.4(n - 1), and that the even-order FE solutions (nis the even number) are unconditionally stable. The consistent domain is also proposed, in which then-order FE solutions are stable and of 2n-order accuracy. Moreover, three-dimensional cases are dealt with, and the comparison with upwind methods is given. The merit and limits of the n-order FE method are finally cleared.