  In this work, we derive a reliable and efficient residual-typed error
estimator for the finite element approximation of a 2d cathodic protection
problem governed by a steady-state diffusion equation with a nonlinear boundary
condition. We propose a standard adaptive finite element method involving the
D\"{o}rfler marking and a minimal refinement without the interior node
property. Furthermore, we establish the contraction property of this adaptive
algorithm in terms of the sum of the energy error and the scaled estimator.
This essentially allows for a quasi-optimal convergence rate in terms of the
number of elements over the underlying triangulation. Numerical experiments are
provided to confirm this quasi-optimality.
