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Adaptive finite element discretization in PDE-based optimization

✍ Scribed by Rolf Rannacher; Boris Vexler

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
224 KB
Volume
33
Category
Article
ISSN
0936-7195

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✦ Synopsis

Abstract

This article surveys recent developments in the adaptive numerical solution of optimal control problems governed by partial differential equations (PDE). By the Euler‐Lagrange formalism the optimization problem is reformulated as a saddle‐point problem (KKT system) that is discretized by a Galerkin finite element method (FEM). Following the Dual Weighted Residual (DWR) approach the accuracy of the approximation is controlled by residual‐based a posteriori error estimates. This opens the way toward systematic complexity reduction in the solution of PDE‐based optimal control problems occurring in science and engineering (Β© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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Solutions to optimization problems with pde constraints inherit special properties; the associated state solves the pde which in the optimization problem takes the role of a equality constraint, and this state together with the associated control solves an optimization problem, i.e. together with mu