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Adaptive Finite Element Methods for Optimal Control Governed by PDEs – Series in Information and Computational Science 41

Author(s): Wenbin Liu, Ningning YAN

Publisher: Science Press
Published Date: 2008
ISBN: 978-7-03-022256-5
Pages: 197
Language: English
Type: Book
Cover: Hard Cover

Our Price: $34.10

Avail: In-Stock

Description

The main idea used in error analysis is to first combine convex analysis and interpolation error estimations of suitable interpolators, whichmuch depend on the structure of the control constraints, in order to derive error estimates for the control via the variational inequalities in the optimality conditions, and then to apply the standard techniques for deriving error estimates for the state equations.

Main Contents

Chapter 1 Introduction
1.1 Examples of optimal control for elliptic systems
1.2 Examples of optimal control for evolution equations
1.3 Examples of optimal control for flow
1.4 Shape optimal control

Chapter 2 Existence and Optimality Conditions of Optimal Control
2.1 Existence of optimal control
2.2 Optimality conditions of optimal control
Chapter 3 Finite Element Approximation of Optimal Control
3.1 Finite element schemes for elliptic optimal control
3.2 Mixed finite element schemes for elliptic optimal control
3.3 Optimal control governed by Stokes equations
3.4 Finite element method for boundary control

Chapter 4 A Priori Error Estimates for Optimal Control (I)
4.1 A priori error estimates for distributed elliptic control
4.2 A priori error estimates for elliptic boundary control
4.3 Superconvergence analysis for distributed elliptic control
4.4 Further developments on superconvergence

Chapter 5 A Priori Error Estimates for Optimal Control (II)
5.1 A priori error estimates of mixed FEM for elliptic control
5.2 Superconvergence of mixed FEM for elliptic control
5.3 A priori error estimates for Stokes control
5.4 Superconvergence for Stokes control

Chapter 6 Adaptivity Finite Element Method for Optimal Control
6.1 Adaptive finite element method for elliptic equations
6.2 Adaptive finite element method for optimal control

Chapter 7 A Posteriori Error Estimates for Optimal Control
7.1 A posteriori error estimates for distributed control
7.2 A posteriori error estimates with lower and upper bounds
7.3 Sharp a posteriori error estimates for constraints of obstacle type
7.4 A posteriori error estimates in L2-norm
7.5 A posteriori error estimates for nonlinear control
7.6 A posteriori error estimates for boundary control

Chapter 8 Numerical Computations of Optimal Control
8.1 Numerical solutions of optimal control
8.2 A preconditioned projection algorithm
8.3 Numerical Experiments
8.4 Appendix-L2-Projectors to some closed convex subsets

Chapter 9 Recovery Based a Posteriori Error
9.1 Equivalence of a posteriori error estimatiors of recovery type
9.2 Asymptotical exactness of a poteriori error estimators of recovery type

Chapter 10 Adaptive mixed finite element method for optimal control
10.1 A posteriori error estimates for elliptic control
10.2 A posteriori error estimates for stokes control
Bibliography