%0 Generic
%A Hesse, Helke Karen
%D 2008
%F heidok:8518
%K Fehlerschätzer , Gittersteuerung , PDEMultiple Shooting , Optimization , PDE , Mesh Adaptation
%R 10.11588/heidok.00008518
%T Multiple Shooting and Mesh Adaptation for PDE Constrained Optimization Problems
%U https://archiv.ub.uni-heidelberg.de/volltextserver/8518/
%X In this thesis, multiple shooting methods for optimization problems constrained by partial differential equations are developed, and, furthermore, a posteriori error estimates and local mesh refinement techniques for these problems are derived. Two different approaches, referred to as the direct and the indirect multiple shooting approach, are developed. While the first approach applies multiple shooting to the constraining equation and sets up the optimality system afterwards, in the latter approach multiple shooting is applied to the optimality system of the optimization problem. The setup of both multiple shooting methods in a function space setting and their discrete analogs are discussed, and different solution and preconditioning techniques are investigated. Furthermore, error representation formulas based on Galerkin orthogonality are derived. They involve sensitivity analysis by means of an adjoint problem and employ standard error representation on subintervals combined with additional projection errors at the shooting nodes. A posteriori error estimates and mesh refinement indicators are derived from this error representation. Several mesh structures originating from different restrictions to local refinement are discussed. Finally, numerical results for the solid state fuel ignition model are presented. This model describes an explosive system that does not allow the solution by standard solution techniques on the whole time domain and is a typical example for the application of time domain decomposition methods like multiple shooting.