Λεπτομέρειες βιβλιογραφικής εγγραφής
| Τίτλος: |
A stochastic Galerkin method for optimal Dirichlet boundary control problems with uncertain data. |
| Συγγραφείς: |
Winkler, Max1 (AUTHOR) max.winkler@mathematik.tu-chemnitz.de, Yücel, Hamdullah2 (AUTHOR) yucelh@metu.edu.tr |
| Πηγή: |
Computational Optimization & Applications. Oct2026, p1-35. 35p. |
| Θεματικοί όροι: |
*Optimal control theory, *Stochastic analysis, Galerkin methods, Approximation error, Numerical analysis, Elliptic differential equations |
| Περίληψη: |
The paper deals with a stochastic Galerkin approximation of elliptic Dirichlet boundary control problems with random input data. The expectation of a tracking-type cost functional with deterministic constrained control is minimized. Error estimates are derived for the control variable in the L2(∂D)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$L^2(\partial {\mathcal {D}})$$\end{document}-norm and for the state variable in the L2(Γ;L2(D))\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${L^2(\Gamma ;L^2({\mathcal {D}}))}$$\end{document}-norm. To solve large linear systems, appropriate preconditioners are proposed for both unconstrained and constrained scenarios. To illustrate the validity and efficiency of the proposed approaches, some numerical experiments are performed. [ABSTRACT FROM AUTHOR] |
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| Βάση Δεδομένων: |
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