Subject: Effiziente Löser für optimales Kontrollproblem für die instationären Stokes Gleichungen im zeitharmonischen Fall
treated by: Wolfgang Krendl
Supervisor: A.Univ.-Prof. Dr. Dipl.-Ing. Walter Zulehner

In this master thesis we study optimal control problems for the Stokes equations with distributed control in the time-dependent and time-harmonic case.

In both cases, where for the time discretization in the time-dependent case we use a discontinuous Galerkin method, the discretized optimality system leads to a very large system of linear equations in saddlepoint form. This linear system depends in a sensitive way on a model parameter α which can be viewed as a regularization or cost parameter.

For the time-harmonic case, we will study, based on recent results from the theory for mixed variational problems, the construction of a block preconditioner, which results in robust convergence rates for the Minimal Residual (MINRES) Method, with respect to the involved model parameters and the mesh size. Finally some numerical tests will illustrate the theoretical results.


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