Adaptive Finite Element Methods for Parameter Identification Problems

The aim of this work is the analysis of parameter identification problems and the development of efficient numerical algorithms for their solution, based on adaptive finite element methods. Since, in general, the computational effort for solving the arising optimization problems exceeds significantly the cost for a simple simulation, the question of choosing efficient (cheap) discretizations is crucial for applications. Our approach to this question is based on the a posteriori error estimation for finite element discretization of the problem. We derive a posteriori error estimators to be used in an adaptive mesh refinement algorithm producing economical meshes for parameter identification. The methods developed in this thesis are applied to parameter identification in fluid dynamics and to estimation of chemical models in multidimensional reactive flow problems