東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回上頁

切換: 標籤 | MARC模式 | ISBD

FindBook

Google Book

Amazon

博客來

Numerical analysis for elliptic optimal control problems

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Numerical analysis for elliptic optimal control problems/ by Boris Vexler, Dominik Meidner.
作者:	Vexler, Boris.
其他作者:	Meidner, Dominik.
出版者:	Cham :Springer Nature Switzerland : : 2025.,
面頁冊數:	xvi, 581 p. :ill., digital ;24 cm.
內容註:	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.
Contained By:	Springer Nature eBook
標題:	Differential equations, Elliptic. -
電子資源:	https://doi.org/10.1007/978-3-031-99316-9
ISBN:	9783031993169

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 ;v. 67..

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

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

541859
Differential equations, Elliptic.

LC Class. No.: QA377

Dewey Class. No.: 518.64

Numerical analysis for elliptic optimal control problems
LDR:02909nmm a2200337 a 4500 001 2421811
003 DE-He213
005 20251014130430.0
006 m d
007 cr nn 008maaau
008 260505s2025 sz s 0 eng d
020 $a 9783031993169 $q (electronic bk.)
020 $a 9783031993152 $q (paper)
024 7 $a 10.1007/978-3-031-99316-9 $2 doi
035 $a 978-3-031-99316-9
040 $a GP $c GP
041 0 $a eng
050 4 $a QA377
072 7 $a PBKS $2 bicssc
072 7 $a MAT041000 $2 bisacsh
072 7 $a PBKS $2 thema
082 0 4 $a 518.64 $2 23
090 $a QA377 $b .V594 2025
100 1 $a Vexler, Boris. $3 3803167
245 1 0 $a Numerical analysis for elliptic optimal control problems $h [electronic resource] / $c by Boris Vexler, Dominik Meidner.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Springer, $c 2025.
300 $a xvi, 581 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer series in computational mathematics, $x 2198-3712 ; $v v. 67
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.
650 0 $a Differential equations, Elliptic. $3 541859
650 0 $a Differential equations, Elliptic $x Numerical solutions. $3 704930
650 0 $a Mathematical optimization. $3 517763
650 1 4 $a Numerical Analysis. $3 892626
650 2 4 $a Mathematics. $3 515831
700 1 $a Meidner, Dominik. $3 3803168
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Springer series in computational mathematics ; $v v. 67. $3 3803169
856 4 0 $u https://doi.org/10.1007/978-3-031-99316-9
950 $a Mathematics and Statistics (SpringerNature-11649)