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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 ( is the odd number) are stable , and that the even-order FE solutions ( is the even number) are unconditionally stable. The consistent domain is also proposed, in which the -order FE solutions are stable and of 2 -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.