Numerical Analysis for Elliptic Optimal Control Problems / by Boris Vexler, Dominik Meidner.

Format:

Book

Author/Creator:

Vexler, Boris.

Contributor:

Meidner, Dominik.

Series:

Springer Series in Computational Mathematics, 2198-3712 ; 67

Language:

English

Subjects (All):

Numerical analysis.

Mathematics.

Numerical Analysis.

Local Subjects:

Numerical Analysis.

Mathematics.

Physical Description:

1 online resource (884 pages)

Edition:

1st ed. 2025.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Springer, 2025.

Summary:

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.

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.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

3-031-99316-0

9783031993169

OCLC:

1545512270