Relative difference between the 2D SG prescriptions and the reference gravitational field (see Eq. (26)) for H = 0.4 AU. From left to right: (left panel) the sharp potential with ε/H = 0, (middle panel) the variable Bessel kernel, and (right panel) the soft potential with ε/H=1.2. The colours of the contour levels at 10⁻⁵, 10⁻³, 0.1, 0.5 are indicated in the colour bar. Softening prescriptions exhibit errors exceeding tens of percent at disc positions, whereas the Bessel prescription maintain errors below 3%.