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Numerical analysis for elliptic optimal control problems

Record Type:	Electronic resources : Monograph/item
Title/Author:	Numerical analysis for elliptic optimal control problemsby Boris Vexler, Dominik Meidner.
Author:	Vexler, Boris.
other author:	Meidner, Dominik.
Published:	Cham :Springer Nature Switzerland :2025.
Description:	xvi, 581 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Differential equations, Elliptic.
Online resource:	https://doi.org/10.1007/978-3-031-99316-9
ISBN:	9783031993169$q(electronic bk.)

Numerical analysis for elliptic optimal control problems
Vexler, Boris.

Numerical analysis for elliptic optimal control problems[electronic resource] /by Boris Vexler, Dominik Meidner. - Cham :Springer Nature Switzerland :2025. - xvi, 581 p. :ill., digital ;24 cm. - Springer series in computational mathematics,v. 672198-3712 ;. - Springer series in computational mathematics ;42..

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.

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.

ISBN: 9783031993169$q(electronic bk.)

Standard No.: 10.1007/978-3-031-99316-9doiSubjects--Topical Terms:

205654
Differential equations, Elliptic.

LC Class. No.: QA377

Dewey Class. No.: 518.64

Numerical analysis for elliptic optimal control problems
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505 0 $a 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.
520 $a 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.
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