Nonlinear diffusion of an initial step function with AMR, the refinement criterion based on radiative energy gradients. a) Radiative energy profiles at time t = 1.4 × 10^-2 (square – numerical solution, “exact” solution in red, run with 2048 cells). The AMR levels (right axis) are plotted in blue. b) L₁ norm of the error as a function of h = 1/Δx, without AMR (diamond) and with AMR (squares), up to an effective resolution of 512 cells (the error is plotted as a function of the minimum mesh spacing, corresponding to the maximum resolution). The dotted line shows the evolution of the error as a function of h².