Adaptive methods for PDE-based optimal control with pointwise inequality constraints [Elektronische Ressource] / vorgelegt von Winnifried Wollner

Inaugural-DissertationzurErlangung der DoktorwürdederNaturwissenschaftlich-Mathematischen GesamtfakultätderRuprecht-Karls-UniversitätHeidelbergvorgelegt vonDiplom-Mathematiker Winnifried Wollneraus Henstedt-UlzburgTag der mündlichen Prüfung: 22.07.2010Adaptive Methods for PDE-based OptimalControl with Pointwise Inequality Constraints19. April 2010Gutachter: Prof. Dr. Rolf RannacherGutachter: Prof. Dr. Hans Georg BockAbstractThis work is devoted to the development of efficient numerical methods for a certain class ofPDE-based optimization problems. The optimization is constraint by an elliptic PDE. Inaddition to prior work in this context pointwise inequality constraints on the control andstate variable are considered. These problems are infinite dimensional and their solution canin general not be obtained exactly. Instead the solution of such problems means to find anapproximate solution. This is done by (approximately) solving for some set of first ordernecessary optimality conditions. Hence an efficient algorithm has to find such an approximatesolution with as little effort as possible while still being accurate enough for whatever thegoal of the computation is.The work at hand contributes to this goal by deriving a posteriori error estimates with respectto a given functional. These estimates are required for two purposes, first, to generate efficientmeshes for the solution of the PDEs required in the process of solving the necessary conditions.