Numerical Analysis for Elliptic Optimal Control Problems
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Beschreibung
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.
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.
Offers a systematic numerical error analysis for discretizing optimal control problems with PDEs Covers a vast array of well-distinguished prototypical optimal control problems Provides all tools form analysis and finite element theory required for treatment of optimal control problems
Autor*in
Boris Vexler
Themen in »Numerical Analysis for Elliptic Optimal Control Problems«
Optimal Control Elliptic PDEs Error Estimates Finite Elements
Stimmen zu »Numerical Analysis for Elliptic Optimal Control Problems«
“The authors chose to cover a reasonable representation of practical situations, keeping a balance with insight and readability. The intended readership are students, researchers and even practitioners that need to solve these kinds of control problems. The contents is accessible for science or engineering students and as much as possible self-contained so that it can be used for self study ... .” (Adhemar Bultheel, zbMATH 1579.49002, 2026)
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