Optimization of technological processes plays an increasing role in science and engineering. This project deals with different types of optimal control problems governed by elliptic or parabolic partial differential equations and characterized by additional pointwise inequality constraints for control and state. Of particular interest are problems with all kinds of singularities including those due to reentrant corners and edges, nonsmooth coefficients, small parameters, and inequality constraints. The project targets two goals: First, starting from a priori error estimates, families of meshes are generated that ensure optimal approximation rates. Second, reliable posteriori error estimators are developed and used for adaptive mesh refinement. A challenge is the incorporation of pointwise inequality constraints for control and state. Both techniques can ensure efficient and reliable numerical results. With a successful strategy it is possible to calculate numerical solutions of the optimal control problems with given accuracy at low cost. While we concentrate on control problems with a linear state equation in this proposal for the first period, we plan to consider semilinear state equations in the second period.
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