Adaptive finite element methods for parameter identification problems [Elektronische Ressource] / vorgelegt von Boris Vexler

Inaugural-DissertationzurErlangung der Doktorwurde¨derNaturwissenschaftlich-Mathematischen Gesamtfakult¨atderRuprecht-Karls-Universit¨atHeidelbergvorgelegt vonDiplom Mathematiker Boris Vexleraus MoskauTag der mundlic¨ hen Prufung:¨ 3. Mai 2004Adaptive Finite Element Methods forParameter Identification ProblemsJanuary 7, 2004Gutachter: Prof. Dr. Rolf RannacherProf. Dr. Hans-Georg Bock4ContentsChapter 1. Introduction 7Chapter 2. Theoretical Results 112.1. Formulation of the problem 112.2. Existence of a solution 132.3. Necessary and sufficient optimality conditions 212.4. Stability and uniqueness of the solution 242.5. Statistical considerations 29Chapter 3. Finite Element Discretization 333.1. Triangulations and finite element spaces 333.2. Discretization of a parameter identification problem 353.3. Existence of a solution of the discrete problem 373.4. A priori error analysis 403.5. Numerical examples 47Chapter 4. Optimization Algorithm 494.1. Newton type methods 494.2. Realizations of the algorithm 514.3. Trust region method 544.4. Numerical examples 57Chapter 5. A Posteriori Error Analysis 615.1. An introductory example 635.2. A posteriori error estimation for the error in parameters 655.3. An extension to more general error functionals 725.4. Localization of the error estimator 745.5. Numerical examples 76Chapter 6. Application to CFD Problems 876.1. Discretization of the Navier-Stokes equations 876.2.