These are some plots:

The first shows the convergence of the 02 mode reducing the size of the mesh. The second shows the the numerical error of the zernike.

The first is found by sweeping a parameter that changes the size of the mesh. The HR surface was set to half a cm for all values.

The second by taking the inner product of a zernike mode with its self and calculating its deviation from pi for varying fineness of the mesh.