Numerical Analysis for Elliptic Optimal Control Problems
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 d...
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| Médium: | Elektronický zdroj E-kniha |
| Jazyk: | angličtina |
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Springer Nature Switzerland : Imprint: Springer,
2025.
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| Vydání: | 1st ed. 2025. |
| Edice: | Springer Series in Computational Mathematics,
67 |
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| On-line přístup: | https://doi.org/10.1007/978-3-031-99316-9 |
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| 100 | 1 | |a Vexler, Boris. |e author. |0 (orcid)0000-0001-6211-4263 |1 https://orcid.org/0000-0001-6211-4263 |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Numerical Analysis for Elliptic Optimal Control Problems |h [electronic resource] / |c by Boris Vexler, Dominik Meidner. |
| 250 | |a 1st ed. 2025. | ||
| 264 | 1 | |a Cham : |b Springer Nature Switzerland : |b Imprint: Springer, |c 2025. | |
| 300 | |a 1 online resource (XVI, 581 p. 1 illus.). | ||
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| 490 | 1 | |a Springer Series in Computational Mathematics, |x 2198-3712 ; |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. | ||
| 532 | 8 | |a Accessibility summary: This PDF has been created in accordance with the PDF/UA-1 standard to enhance accessibility, including screen reader support, described non-text content (images, graphs), bookmarks for easy navigation, keyboard-friendly links and forms and searchable, selectable text. We recognize the importance of accessibility, and we welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us at accessibilitysupport@springernature.com. Please note that a more accessible version of this eBook is available as ePub. | |
| 532 | 8 | |a No reading system accessibility options actively disabled | |
| 532 | 8 | |a Publisher contact for further accessibility information: accessibilitysupport@springernature.com | |
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| 650 | 0 | |a Numerical analysis. | |
| 650 | 0 | |a Mathematics. | |
| 650 | 1 | 4 | |a Numerical Analysis. |
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| 700 | 1 | |a Meidner, Dominik. |e author. |0 (orcid)0000-0002-4949-6356 |1 https://orcid.org/0000-0002-4949-6356 |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
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| 830 | 0 | |a Springer Series in Computational Mathematics, |x 2198-3712 ; |v 67 | |
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