Experiment with known solution from Section 8.4: Convergence of |$\eta_\ell(u_\ell)$| (solid lines) and |$\left\| {{\nabla u^\star - \nabla u_\ell}} \right\|_{L^2(\varOmega)}$| (dashed lines) for |$\lambda = 10^{-5}$| and different values of |$\theta\in\{0.2,\dots, 1 \}$|⁠, where we compare naive initial guesses |$u_\ell^0 := 0$| (left) and nested iteration |$u_\ell^0 := u_{\ell-1}$| (right).