Finite element steady-state solutions of the traveling magnetic field problem

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 (
n
is the odd number) are stable
0 < \sigma|u|h|\nu < f(n) \simeq 2.0 + 1.4(n - 1)
, and that the even-order FE solutions (
n
is the even number) are unconditionally stable. The consistent domain is also proposed, in which the
n
-order FE solutions are stable and of 2
n
-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.