Abstract: Rolf Rannacher

Heidelberg University

Adaptive FEM Discretization in Solving PDE-based Optimization Problems

We address the basics and recent developments of "goal-oriented" adaptivity by the Dual Weighted Residual (DWR) method for the solution of PDE-based optimization problems. By the Lagrangian formalism the optimization problem is reformulated as a saddle-point boundary value problem (KKT system) that is discretized by a Galerkin finite element method. The accuracy of the discretization is controlled by residual-based a posteriori error estimates which contain primal and dual cell-residuals and associated sensitivity factors. The resulting local error indicators then assist the construction of economical meshes for evaluating and optimizing the quantities of physical interest. This opens the way towards systematic model reduction in the solution of optimization problems. The main features of this approach will be illustrated by examples from flow control and parameter estimation. Recent developments concern the inclusion of control and state constraints, the treatment of nonstationary optimal control problems, the balancing of discretization and iteration errors, and the adaptive choice of regularization parameters.


 

Aachen Institute for Advanced Study in Computational Engineering Science (AICES)
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