German Title: Adaptive Finite-Elemente-Methoden zur Identifikation verteilter Parameter in partiellen Differentialgleichungen
Translation of abstract (English)
In this thesis, we develop algorihms for the solution of inverse problems by the adaptive finite element method. In particular, we consider problems where distributed coefficients in partial differential equations are to be identified from measurements of the state variable. The ingredients for efficient algorithms are error estimates for various quantities, such as the misfit or the error in the coefficient, and adaptive finite element discretization strategies. We also discuss the numerical solution of the resulting discrete equations, as well as the incorporation of inequality constraints on the sought coefficient. The efficiency of the proposed methods is verified at a number of synthetic examples.
|Supervisor:||Rannacher, Professor Rolf|
|Date of thesis defense:||12 July 2002|
|Faculties / Institutes:||The Faculty of Mathematics and Computer Science > Department of Applied Mathematics|
|Controlled Keywords:||Numerische Mathematik, System mit verteilten Parametern, Finite-Elemente-Methode|
|Uncontrolled Keywords:||Numerical analysis , Distributed parameter systems , Finite element method|