I've written some code that carries out the central finite difference equation to solve this poisson system:
$\Delta u(x,y) = f, u(x,y) = g$ in domain $[0,1]^2$.
where $u(x,y) = \cos(4) \cos(4)$ (and hence $\Delta u = -32\pi^2\cos(4) \cos(4)$)
I get this contour plot of my results:
And for some reason I have an increasing gridpoint L2 norm as N increases. I know my code is correct as when I test it with any other similar function I get a smooth contour as expected. Would anyone be able to shine some light on what could be going on?