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{\large Stefan Ulbrich \\
{\bf Adaptive multilevel methods for time-dependent PD(A)E-constrained optimization with control constraints}}

Technische Universitaet Darmstadt \\ Department of Mathematics \\ Dolivostr 15 \\ 64293 Darmstadt
\\
{\tt ulbrich@mathematik.tu-darmstadt.de}\\
Debora Clever\\
Jens Lang\\
Jan Carsten Ziems\end{center}

We present an adaptive multilevel generalized SQP-method for optimal
control problems governed by nonlinear time-dependent PD(A)Es with
control constraints. Starting with a coarse discretization we combine a
generalized trust-region SQP method with an implementable adaptive
refinement strategy based on error estimators for the PD(A)E, adjoint
PD(A)E and a criticality measure. Moreover, we discuss a variant based on
goal oriented error estimators. The algorithm supports the use of
independent discretization for the state and adjoint PD(A)E. We show
numerical results, where our multilevel SQP-method is in particular
coupled with the space-time adaptive PDAE solver KARDOS.


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