Starting with several typical examples of optimal control problems Adaptive Finite Element Methods covers the numerous complexities of the subject, emphasizing the discussions of some unique issues from the adaptive finite element approximation of optimal control. The book highlights the main ideas used in the approximation error analysis in order 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 are emphasized throughout the book, as are the finite element approximation schemes for several typical optimal control problems alongside the derivation of their a priori and a posteriori error estimate.

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

About the Author

Wenbin Liu.: University of Kent, U.K. Ningning Yan.: Academy of Mathematics and Systems Sciences Chinese Academy of Sciences, China

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