Adaptive Finite Element Methods: Optimal Control Governed by PDEs
Author(s): Wenbin Liu, Ningning Yan
E-ISBN: Publication Year: 2012
Binding: Hard Back Dimension: 160mm x 240mm Weight: 500
About the book
ADAPTIVE FINITE ELEMENT METHODS: Optimal Control Governed by PDEs emphasizes the discussions of some unique issues from the adaptive finite element approximation of optimal control. The main idea used in the approximation error analysis (both a priori and a posteriori) is to first combine convex analysis and interpolation error estimations of suitable interpolators, which depend on the structure of the control constraints, to derive the error estimates for the control via the variational inequalities in the optimality conditions, and then to apply the standard techniques to derive the error estimates for the state equations. The need, the framework and the techniques of using multi adaptive meshes in developing efficient numerical algorithms for optimal control have been emphasized throughout the book. The book starts from several typical examples of optimal control problems and then discusses existence and optimality conditions for some optimal control problems. Then the finite element approximation schemes for several typical optimal control problems are set up, their a priori and a posteriori error estimates are derived following the main idea mentioned, and their computational methods are studied.
Table of Contents
Introduction / Existence and Optimality Conditions of Optimal Control / Finite Element Approximation of Optimal Control / A Priori Error Estimates for Optimal Control (I) / A Priori Error Estimates for Optimal Control (II) / Adaptivity Finite Element Method for Optimal Control / A Posteriori Error Estimates for Optimal Control / Numerical Computations of Optimal Control / Recovery Based a Posteriori Error Estimators / Adaptive Mixed Finite Element Method for Optimal Control / Bibliography