This paper is concerned with the discretization error analysis of semilinear
Neumann boundary control problems in polygonal domains with pointwise
inequality constraints on the control. The approximations of the control are
piecewise constant functions. The state and adjoint state are discretized by
piecewise linear finite elements. In a postprocessing step approximations of
locally optimal controls of the continuous optimal control problem are
constructed by the projection of the respective discrete adjoint state.
Although the quality of the approximations is in general affected by corner
singularities a convergence order of h2β£lnhβ£3/2 is proven for domains
with interior angles smaller than 2Ο/3 using quasi-uniform meshes. For
larger interior angles mesh grading techniques are used to get the same order
of convergence