If your negative values are due to numerical stabilization issues due to convection dominating terms it should also help to use monotonicity preserving FEM-TVD stabilization which can be switched on using the "Shock-Capturing" option in the "Artificial Stabilization" options dialog box:
https://www.featool.com/doc/physics.html#phys_artstabBut aside from that PDE problems are generally too complex for completely automatic reformulation of this type.