Existence of boundary error transverse to the velocity in SU/PG solution of moving conductor problem

In the simulation of moving-conductor problems, the widely employed Galerkin finite element method is known to suffer from numerical instabilities. The streamline upwinding/Petrov-Galerkin (SU/PG) scheme is generally employed to overcome this problem. Unfortunately, in the fluid dynamics literature the SU/PG scheme is known to introduce boundary errors transverse to the flow. In this work, the existence of such an error in the SU/PG solution of moving conductor problem is investigated, probably for the first time. An attempt is also made to quantify the error in a simplified 2D problem.