If you want to do a test, try classical shapes that have analytical solutions and compare with your simulator. This will also show the effects of simulation element size on accuracy.
Some classical shapes are coaxial cable with both conductors round, two conductor in circular shield, and coaxial with square outer conductor.
How about the solution of multilayer structure
with lossy (finite conductivity) material?
Is there any closed-form equation to calculate
conductance & capacitance (not closed-form Green's function)
for a classic structure, such as a metal-SiO2-Si microstrip
or CPW?