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**Harvard**

Kraft, K. (2011) *Adaptive Finite Element Methods for Optimal Control Problems*. Göteborg : Chalmers University of Technology (Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie, nr: 3175).

** BibTeX **

@book{

Kraft2011,

author={Kraft, Karin},

title={Adaptive Finite Element Methods for Optimal Control Problems},

isbn={978-91-7385-494-811},

abstract={In this thesis we study the numerical solution of
optimal control problems. The problems considered consist of a system
of differential equations, the state equations, which are governed by
a control variable. The goal is to determine the states and controls which minimize a given cost functional.
The numerical method in this work is based on an indirect approach,
which means that necessary conditions for optimality are first derived
and then solved numerically, in our case by a finite element method.
The optimality conditions are derived using
Lagrange's method in the calculus of variations resulting in a boundary value
problem for a system of differential/algebraic equations. These
equations are discretized by a finite element method. The advantage of
the finite element method is the possibility to use functional
analysis to derive error estimates and in this work this is used
to prove computable a posteriori error estimates. The error estimates are
derived in the framework of dual weighted residuals which is well
suited for optimal control problems since it is formulated within the
Lagrange framework.
Using an indirect method combined with an a posteriori error
estimate makes it possible to implement adaptive finite element
methods where the refinement of the computational mesh is
automated. We have implemented such adaptive finite element methods for quadratic/linear optimal control
problems, fully nonlinear problems, and for problems with inequality
constraints on controls and states.},

publisher={Institutionen för matematiska vetenskaper, matematik, Chalmers tekniska högskola,},

place={Göteborg},

year={2011},

series={Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie, no: 3175},

keywords={finite element method, discontinuous Galerkin method, optimal control, a posteriori error estimate, dual weighted residual, adaptive, multilevel algorithm, Newton method, control constraint, variational inequality, vehicle dynamics.},

note={105},

}

** RefWorks **

RT Dissertation/Thesis

SR Electronic

ID 136193

A1 Kraft, Karin

T1 Adaptive Finite Element Methods for Optimal Control Problems

YR 2011

SN 978-91-7385-494-811

AB In this thesis we study the numerical solution of
optimal control problems. The problems considered consist of a system
of differential equations, the state equations, which are governed by
a control variable. The goal is to determine the states and controls which minimize a given cost functional.
The numerical method in this work is based on an indirect approach,
which means that necessary conditions for optimality are first derived
and then solved numerically, in our case by a finite element method.
The optimality conditions are derived using
Lagrange's method in the calculus of variations resulting in a boundary value
problem for a system of differential/algebraic equations. These
equations are discretized by a finite element method. The advantage of
the finite element method is the possibility to use functional
analysis to derive error estimates and in this work this is used
to prove computable a posteriori error estimates. The error estimates are
derived in the framework of dual weighted residuals which is well
suited for optimal control problems since it is formulated within the
Lagrange framework.
Using an indirect method combined with an a posteriori error
estimate makes it possible to implement adaptive finite element
methods where the refinement of the computational mesh is
automated. We have implemented such adaptive finite element methods for quadratic/linear optimal control
problems, fully nonlinear problems, and for problems with inequality
constraints on controls and states.

PB Institutionen för matematiska vetenskaper, matematik, Chalmers tekniska högskola,

T3 Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie, no: 3175

LA eng

LK http://publications.lib.chalmers.se/records/fulltext/136193.pdf

OL 30