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Numerical Functional Analysis and Optimization Volume 28, 2007 - Issue 7-8
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Original Articles

Finite Element Approximation of Elliptic Dirichlet Optimal Control Problems

B. Vexler Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Linz, AustriaCorrespondence[email protected]
Pages 957-973 | Published online: 13 Aug 2007

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Quanxiang Wang, Jianqiang Xie & Zhiyue Zhang. (2022) Nonconforming immersed finite element method for solving elliptic optimal control problems with interfaces. Applicable Analysis 101:6, pages 2197-2216.
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Xiuxiu Lin, Mengya Su & Zhiyue Zhang. (2020) Fourier Finite Volume Element Method for Two Classes of Optimal Control Problems Governed by Elliptic PDEs on Complex Connected Domain. Numerical Functional Analysis and Optimization 41:4, pages 379-412.
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Pablo Gamallo, Erwin Hernández & Andrés Peters. (2011) On the Error Estimates for the Finite Element Approximation of a Class of Boundary Optimal Control Systems. Numerical Functional Analysis and Optimization 32:4, pages 383-396.
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Articles from other publishers (27)

Wenju Liu, Tengjin Zhao, Kazufumi Ito & Zhiyue Zhang. (2023) Error estimates of Fourier finite volume element method for parabolic Dirichlet boundary optimal control problems on complex connected domains. Applied Numerical Mathematics 186, pages 164-201.
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Qian Zhang & Zhiyue Zhang. (2023) Nitsche’s method for elliptic Dirichlet boundary control problems on curved domains. Numerical Algorithms.
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Shaohong Du & Xiaoxia He. (2023) Finite element approximation to optimal Dirichlet boundary control problem: A priori and a posteriori error estimates. Computers & Mathematics with Applications 131, pages 14-25.
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Mengya Su, Liuqing Xie & Zhiyue Zhang. (2022) Numerical Analysis of Fourier Finite Volume Element Method for Dirichlet Boundary Optimal Control Problems Governed by Elliptic PDEs on Complex Connected Domains. Mathematics 10:24, pages 4779.
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Woocheol Choi & Young-Pil Choi. (2022) A sharp error analysis for the DG method of optimal control problems. AIMS Mathematics 7:5, pages 9117-9155.
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Shaohong Du & Zhiqiang Cai. (2021) Adaptive Finite Element Method for Dirichlet Boundary Control of Elliptic Partial Differential Equations. Journal of Scientific Computing 89:2.
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Hamdullah Yücel. (2021) Goal–oriented a posteriori error estimation for Dirichlet boundary control problems. Journal of Computational and Applied Mathematics 381, pages 113012.
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Wei Gong & Buyang Li. (2020) Improved error estimates for semidiscrete finite element solutions of parabolic Dirichlet boundary control problems. IMA Journal of Numerical Analysis 40:4, pages 2898-2939.
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Weiwei Hu, Jiguang Shen, John R. Singler, Yangwen Zhang & Xiaobo Zheng. (2019) A superconvergent hybridizable discontinuous Galerkin method for Dirichlet boundary control of elliptic PDEs. Numerische Mathematik 144:2, pages 375-411.
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Jun Liu. (2019) Two fast finite difference schemes for elliptic Dirichlet boundary control problems. Journal of Applied Mathematics and Computing 61:1-2, pages 481-503.
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Erik Burman, Peter Hansbo & Mats G Larson. (2018) Solving ill-posed control problems by stabilized finite element methods: an alternative to Tikhonov regularization. Inverse Problems 34:3, pages 035004.
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Wei Gong, Weiwei Hu, Mariano Mateos, John Singler, Xiao Zhang & Yangwen Zhang. (2018) A New HDG Method for Dirichlet Boundary Control of Convection Diffusion PDEs II: Low Regularity. SIAM Journal on Numerical Analysis 56:4, pages 2262-2287.
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Wei Gong, Michael Hinze & Zhaojie Zhou. (2015) Finite Element Method and A Priori Error Estimates for Dirichlet Boundary Control Problems Governed by Parabolic PDEs. Journal of Scientific Computing 66:3, pages 941-967.
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G. Of, T. X. Phan & O. Steinbach. (2014) An energy space finite element approach for elliptic Dirichlet boundary control problems. Numerische Mathematik 129:4, pages 723-748.
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Federico Negri, Andrea Manzoni & Gianluigi Rozza. (2015) Reduced basis approximation of parametrized optimal flow control problems for the Stokes equations. Computers & Mathematics with Applications 69:4, pages 319-336.
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G. Deolmi & F. Marcuzzi. (2013) A parabolic inverse convection?diffusion?reaction problem solved using space?time localization and adaptivity. Applied Mathematics and Computation 219:16, pages 8435-8454.
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Bülent Karasözen & Hamdullah Yücel. 2013. Chaos and Complex Systems. Chaos and Complex Systems 83 94 .
Günther Of, Thanh Xuan Phan & Olaf Steinbach. 2012. Modeling, Simulation and Optimization of Complex Processes. Modeling, Simulation and Optimization of Complex Processes 219 231 .
Michael Hinze & Arnd Rösch. 2012. Constrained Optimization and Optimal Control for Partial Differential Equations. Constrained Optimization and Optimal Control for Partial Differential Equations 391 430 .
Wei Gong & Ningning Yan. (2011) Mixed Finite Element Method for Dirichlet Boundary Control Problem Governed by Elliptic PDEs. SIAM Journal on Control and Optimization 49:3, pages 984-1014.
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Axel Kröner, Karl Kunisch & Boris Vexler. (2011) Semismooth Newton Methods for Optimal Control of the Wave Equation with Control Constraints. SIAM Journal on Control and Optimization 49:2, pages 830-858.
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Günther Of, Thanh Xuan Phan & Olaf Steinbach. (2010) Boundary element methods for Dirichlet boundary control problems. Mathematical Methods in the Applied Sciences 33:18, pages 2187-2205.
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Michael Hinze & Fredi Tröltzsch. (2010) Discrete concepts versus error analysis in PDE‐constrained optimization. GAMM-Mitteilungen 33:2, pages 148-162.
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K. Krumbiegel, C. Meyer & A. Rösch. (2010) A Priori Error Analysis for Linear Quadratic Elliptic Neumann Boundary Control Problems with Control and State Constraints. SIAM Journal on Control and Optimization 48:8, pages 5108-5142.
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Fredi Tröltzsch. 2010. Large-Scale Scientific Computing. Large-Scale Scientific Computing 40 53 .
Klaus Deckelnick, Andreas Günther & Michael Hinze. (2009) A priori estimates for optimal Dirichlet boundary control problems. PAMM 9:1, pages 611-612.
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Klaus Deckelnick, Andreas G?nther & Michael Hinze. (2009) Finite Element Approximation of Dirichlet Boundary Control for Elliptic PDEs on Two- and Three-Dimensional Curved Domains. SIAM Journal on Control and Optimization 48:4, pages 2798-2819.
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