  For the simulation of rectilinearly moving conductors across a magnetic
field, the Galer-kin finite element method (GFEM) is generally employed. The
inherent instability of GFEM is very often addressed by employing Streamline
upwinding/Petrov-Galerkin (SU/PG) scheme. However, the SU/PG solution is known
to suffer from distortion at the boundary transverse to the velocity and the
remedial measures suggested in fluid dynamics literature are computationally
demanding. Therefore, simple alternative schemes are essential. In an earlier
effort, instead of conventional finite-difference based approach, the numerical
instability was analyzed using the Z-transform. By employing the concept of
pole-zero cancellation, stability of the numerical solution was achieved by a
simple restatement of the input magnetic flux in terms of associated vector
potential. This approach, however, is restricted for input fields, which vary
only along the direction of the velocity. To overcome this, the present work
proposes a novel approach in which the input field is restated as a weighted
elemental average. The stability of the proposed scheme is proven analytically
for both 1D and 2D cases. The error bound for the small oscillations remnant at
intermittent Peclet numbers is also deduced. Using suitable numerical
simulations, all the theoretical deductions are verified.
