singular electric field

Hi all

Im facing a singularity issue as Im calculating magnetic field of conduction current inside a microchannel flow. The reason I get a locally high magnetic field even if the corners are rounded is that the expression that I use for the current is singular in points (there is gradient of potential inside conduction current). This in turn happens because I have applied a zero surface charge density on one side of these points, and a non-zero surface charge density on the other side. The result is a singular electric field. please see attached image.

is there a way around this problem ?

Thank you
Abraham