  The finite element method is one of the widely employed numerical techniques
in electrical engineering for the study of electric and magnetic fields. When
applied to the moving conductor problems, the finite element method is known to
have numerical oscillations in the solution. To resolve this, the upwinding
techniques, which are developed for the transport equation are borrowed and
directly employed for the magnetic induction equation. In this work, an
alternative weighted residual formulation is explored for the simulation of the
linear moving conductor problems. The formulation is parameter-free and the
stability of the formulation is analytically studied for the 1D version of the
moving conductor problem. Then the rate of convergence and the accuracy are
illustrated with the help of several test cases in 1D as well as 2D.
Subsequently, the stability of the formulation is demonstrated with a 3D moving
conductor simulation.
