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M1

FWF/DFG Project within priority program 1253

Numerical analysis and discretization strategies for optimal control problems with singularities

Funding Periods

Project Abstract

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 lead to efficient and reliable numerical results and allow to calculate numerical solutions of the optimal control problems with given accuracy at a small multiple of the cost of the pure numerical simulation. While the first period of the project was mainly devoted to problems with a linear elliptic state equation, we will consider semilinear and parabolic state equations in the second period. As a non-standard application with a parabolic semilinear state equation and inequality constraints, we will continue to model, analyze and simulate the optimization of the thermo-mechanic properties of concrete during hydration.

Keywords and AMS Classification

AMS Subject Classification: 49K20, 49M25, 49N10, 49N60

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