This thesis deals with pointwise error estimates for finite element discretizations of boundary control problems on general polygonal domains, namely, the Neumann control problem and the Dirichlet control problem with constant control constraints. In order to show the quasi-optimal convergence rate h²|ln h| in the L∞-Norm for the discretizations of the Neumann control problem, first, this rate is derived for the piecewise linear discretization of the Neumann boundary value problems. We achieve this goal by exploiting graded meshes which compensate the singular behavior of the solution in the vicinity of corner points. Best possible rates of convergence on quasi-uniform meshes are also shown. For the numerical analysis of the Neumann optimal control problem two discretization strategies are considered, namely, the variational discretization and the postprocessing approach. In both cases the quasi-optimal rate on graded meshes and best possible rates on quasi-uniform meshes are shown. The numerical analysis for the Dirichlet optimal control problem is performed only on quasi-uniform meshes. Best possible convergence order for the piecewise linear approximation of the control is obtained on convex domains. All the theoretical results in this work are justified by numerical experiments.     «

This thesis deals with pointwise error estimates for finite element discretizations of boundary control problems on general polygonal domains, namely, the Neumann control problem and the Dirichlet control problem with constant control constraints. In order to show the quasi-optimal convergence rate h²|ln h| in the L∞-Norm for the discretizations of the Neumann control problem, first, this rate is derived for the piecewise linear discretization of the Neumann boundary value problems. We achieve t...     »