Error and refinement
 

I'm trying to plot the error vs grid size for a 3D simple unit cube for the steady state heat equation. When I increase the number of iterations linearly with the number of points for successive refinement levels, I get an decrease in the error for smaller refinements. This seems right, but when I iterate until convergence (residual converge 1e-9), I get that the error increases with smaller refinements. Could this be right? Shouldn't the residual be of the same magnitude (order) as the error? The error seems to increase from 1e-9 to 1e-7 when the refinements go from 1/2 to 1/20, see figure.