Subject of this thesis is the numerical analysis of optimal control problems with linear and semilinear elliptic partial differential equations in polygonal domains. It is assumed that the control acts on the Neumann boundary and additionally fulfills point-wise inequality constraints. As discretization strategies the concept of variational discretization and the postprocessing approach are considered. The numerical analysis for both approaches relies on finite element error estimates in the $L^2$-norm on the boundary for the linear elliptic boundary value problem. The first contribution of this work is the proof of quasi-optimal error estimates for quasi-uniform meshes. There it turns out that the convergence order decreases in general due to the appearance of corner singularities starting from a certain size of the interior angles of the polygonal domain. Therefore, gradually refined meshes, which compensate this effect, are analyzed in addition. Beyond that, it is demonstrated how these results can be transferred to semilinear elliptic boundary value problems. Then for linear as well as for semilinear elliptic Neumann boundary control problems quasi-optimal convergence rates are proven for both discretization strategies by using the obtained error estimates on the boundary. All theoretical results for the boundary value problems and the optimal control problems are confirmed by numerical examples.     «

Subject of this thesis is the numerical analysis of optimal control problems with linear and semilinear elliptic partial differential equations in polygonal domains. It is assumed that the control acts on the Neumann boundary and additionally fulfills point-wise inequality constraints. As discretization strategies the concept of variational discretization and the postprocessing approach are considered. The numerical analysis for both approaches relies on finite element error estimates in the $L^...     »