Abstract:

In this thesis, we develop adaptive finite element methods for parameter estimation problems involving partial differential equations as constraints. In these so-called Inverse Problems, the goal is the identification of a distributed coefficient in a PDE by measurements of the state variable. This has important applications where material parameters are to be recovered, but only indirect measurements are possible, such as identification of the underground structure from seismic measurements, or in nondestructive material testing.

For this kind of problems, we develop adaptive finite element discretizations based on error estimates, where the estimates are both for the error in the minimization functional (i.e. of ``energy-type'') as well as in arbitrary functionals. Furthermore, methods are developed to handle constraints on the sought coefficients, based on active set strategies. The methods developed are numerically tested at a number of large scale inverse problems realizing some types of inverse problems that actually occur in applications.



Wolfgang Bangerth
2002-04-16