NDLI: Adaptive Finite Element Methods for Optimal Control of Partial Differential Equations: Basic Concept

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Rannacher, Rolf Becker, Roland Kapp, Hartmut
Copyright Year	2000
Abstract	A new approach to error control and mesh adaptivity is described for the discretization of optimal control problems governed by elliptic partial differential equations. The Lagrangian formalism yields the first-order necessary optimality condition in form of an indefinite boundary value problem which is approximated by an adaptive Galerkin finite element method. The mesh design in the resulting reduced models is controlled by residual-based a posteriori error estimates. These are derived by duality arguments employing the cost functional of the optimization problem for controlling the discretization error. In this case, the computed state and costate variables can be used as sensitivity factors multiplying the local cell-residuals in the error estimators. This results in a generic and simple algorithm for mesh adaptation within the optimization process. This method is developed and tested for simple boundary control problems in semiconductor models.
Starting Page	113
Ending Page	132
Page Count	20
File Format	PDF
ISSN	03630129
DOI	10.1137/S0363012999351097
e-ISSN	10957138
Issue Number	1
Volume Number	39
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-26
Access Restriction	Subscribed
Subject Keyword	optimal control problem mesh adaptation Optimization and variational techniques model reduction a posteriori error estimates Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods finite elements Problems involving partial differential equations
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Applied Mathematics

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