Numerical Analysis for Elliptic Optimal Control Problems
Series: Springer Series in Computational Mathematics; 67;
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Product details:
- Publisher Springer Nature Switzerland
- Date of Publication 15 October 2025
- Number of Volumes 1 pieces, Book
- ISBN 9783031993152
- Binding Hardback
- No. of pages581 pages
- Size 235x155 mm
- Language English
- Illustrations XVI, 581 p. 1 illus. 695
Categories
Long description:
This book presents a systematic approach to the numerical analysis of several carefully selected classes of optimal control problems governed by elliptic partial differential equations (PDEs). A priori error estimates for the discretization error between the optimal solutions of the continuous and discretized problems are derived, and numerical experiments are included to illustrate the results.
The proofs are presented in a structured and accessible manner, facilitating a clear understanding of the techniques used. The necessary results from functional analysis and elliptic PDE theory are provided in a self-contained way. Essential aspects of finite element theory—including some results newly established by the author(s)—are also covered, with all relevant proofs provided in full detail.
Portions of the material have been successfully used in graduate-level courses and seminars, as well as in Master’s and PhD theses. The book is intended for researchers and graduate students interested in finite element analysis and/or optimal control problems involving PDEs.
Table of Contents:
Chapter 1. Introduction.- Part I. Theory and Finite Elements for Elliptic PDEs.- Chapter 2. Topics from the Theory of Elliptic PDEs.- Chapter 3. Topics from Finite Elements for Elliptic PDEs.- Part II. Distributed Control Problems.- Chapter 4. No Inequality Constraints.- Chapter 5. Control Constraints.- Chapter 6. Bang-Bang Controls.- Chapter 7. Semilinear State Equation.- Part III. Boundary Control Problems.- Chapter 8. Neumann Control.- Chapter 9. Dirichlet Control.- Part IV. Problems Involving Dirac Measures.- Chapter 10. Pointwise Control.- Chapter 11. Pointwise Tracking.- Chapter 12. Finitely Many Pointwise State Constraints.- Part V. Problems Involving General Measures.- Chapter 13. State Constraints.- Chapter 14. Sparse Controls.
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