Space-Time Finite Element Discretization of Parabolic Optimal Control Problems with Energy Regularization

Ulrich Langer; Olaf Steinbach; Fredi Tröltzsch; Huidong Yang

doi:10.1137/20m1332980

Space-Time Finite Element Discretization of Parabolic Optimal Control Problems with Energy Regularization

SIAM Journal on Numerical Analysis ◽

10.1137/20m1332980 ◽

2021 ◽

Vol 59 (2) ◽

pp. 675-695

Author(s):

Ulrich Langer ◽

Olaf Steinbach ◽

Fredi Tröltzsch ◽

Huidong Yang

Keyword(s):

Optimal Control ◽

Finite Element ◽

Optimal Control Problems ◽

Space Time ◽

Control Problems ◽

Finite Element Discretization ◽

Element Discretization ◽

Parabolic Optimal Control

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A Priori Error Analysis for Space-Time Finite Element Discretization of Parabolic Optimal Control Problems

Numerical Mathematics and Advanced Applications ◽

10.1007/978-3-540-69777-0_77 ◽

2008 ◽

pp. 645-652

Author(s):

D. Meidner ◽

B. Vexler

Keyword(s):

Optimal Control ◽

Finite Element ◽

Error Analysis ◽

Optimal Control Problems ◽

A Priori ◽

Space Time ◽

Control Problems ◽

Finite Element Discretization ◽

Element Discretization ◽

Parabolic Optimal Control

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A priori error estimates for space–time finite element discretization of semilinear parabolic optimal control problems

Numerische Mathematik ◽

10.1007/s00211-011-0409-9 ◽

2011 ◽

Vol 120 (2) ◽

pp. 345-386 ◽

Cited By ~ 36

Author(s):

Ira Neitzel ◽

Boris Vexler

Keyword(s):

Optimal Control ◽

Finite Element ◽

Optimal Control Problems ◽

A Priori ◽

Control Problems ◽

Finite Element Discretization ◽

Element Discretization ◽

Priori Error Estimates ◽

Parabolic Optimal Control ◽

Semilinear Parabolic

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A Priori Error Estimates for Space-Time Finite Element Discretization of Parabolic Optimal Control Problems Part I: Problems Without Control Constraints

SIAM Journal on Control and Optimization ◽

10.1137/070694016 ◽

2008 ◽

Vol 47 (3) ◽

pp. 1150-1177 ◽

Cited By ~ 78

Author(s):

Dominik Meidner ◽

Boris Vexler

Keyword(s):

Optimal Control ◽

Finite Element ◽

Optimal Control Problems ◽

A Priori ◽

Control Problems ◽

Control Constraints ◽

Finite Element Discretization ◽

Element Discretization ◽

Priori Error Estimates ◽

Parabolic Optimal Control

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A new iterative method for solving the systems arisen from finite element discretization of a time-harmonic parabolic optimal control problems

Mathematics and Computers in Simulation ◽

10.1016/j.matcom.2021.02.013 ◽

2021 ◽

Vol 185 ◽

pp. 771-782

Author(s):

Hamid Mirchi ◽

Davod Khojasteh Salkuyeh

Keyword(s):

Optimal Control ◽

Finite Element ◽

Iterative Method ◽

Optimal Control Problems ◽

Control Problems ◽

Finite Element Discretization ◽

Element Discretization ◽

Time Harmonic ◽

Parabolic Optimal Control ◽

New Iterative Method

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A Priori Error Estimates for Space-Time Finite Element Discretization of Parabolic Optimal Control Problems Part II: Problems with Control Constraints

SIAM Journal on Control and Optimization ◽

10.1137/070694028 ◽

2008 ◽

Vol 47 (3) ◽

pp. 1301-1329 ◽

Cited By ~ 91

Author(s):

Dominik Meidner ◽

Boris Vexler

Keyword(s):

Optimal Control ◽

Finite Element ◽

Optimal Control Problems ◽

A Priori ◽

Control Problems ◽

Control Constraints ◽

Finite Element Discretization ◽

Element Discretization ◽

Priori Error Estimates ◽

Parabolic Optimal Control

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A Priori Error Estimates for Space-Time Finite Element Discretization of Parabolic Optimal Control Problems

Constrained Optimization and Optimal Control for Partial Differential Equations ◽

10.1007/978-3-0348-0133-1_23 ◽

2011 ◽

pp. 445-466

Author(s):

Dominik Meidner ◽

Boris Vexler

Keyword(s):

Optimal Control ◽

Finite Element ◽

Error Estimates ◽

Optimal Control Problems ◽

A Priori ◽

A Priori Error Estimates ◽

Finite Element Discretization ◽

Element Discretization ◽

Priori Error Estimates ◽

Parabolic Optimal Control

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A New Conical Regularization for Some Optimization and Optimal Control Problems: Convergence Analysis and Finite Element Discretization

Numerical Functional Analysis and Optimization ◽

10.1080/01630563.2013.806546 ◽

2013 ◽

Vol 34 (8) ◽

pp. 861-895 ◽

Cited By ~ 6

Author(s):

Akhtar A. Khan ◽

Miguel Sama

Keyword(s):

Optimal Control ◽

Finite Element ◽

Convergence Analysis ◽

Optimal Control Problems ◽

Control Problems ◽

Finite Element Discretization ◽

Element Discretization ◽

Optimization And Optimal Control

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A Priori Error Estimates for Space-Time Finite Element Discretization of Parabolic Time-Optimal Control Problems

SIAM Journal on Control and Optimization ◽

10.1137/18m1166948 ◽

2019 ◽

Vol 57 (1) ◽

pp. 129-162 ◽

Cited By ~ 1

Author(s):

Lucas Bonifacius ◽

Konstantin Pieper ◽

Boris Vexler

Keyword(s):

Optimal Control ◽

Finite Element ◽

Error Estimates ◽

Optimal Control Problems ◽

A Priori ◽

Control Problems ◽

Finite Element Discretization ◽

Element Discretization ◽

Time Optimal ◽

Priori Error Estimates

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A robust optimal preconditioner for the mixed finite element discretization of elliptic optimal control problems

Numerical Linear Algebra with Applications ◽

10.1002/nla.2129 ◽

2017 ◽

Vol 25 (1) ◽

pp. e2129

Author(s):

Wei Gong ◽

Zhiyu Tan ◽

Shuo Zhang

Keyword(s):

Optimal Control ◽

Finite Element ◽

Optimal Control Problems ◽

Mixed Finite Element ◽

Control Problems ◽

Finite Element Discretization ◽

Element Discretization ◽

Elliptic Optimal Control Problems ◽

Elliptic Optimal Control

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Finite Element Discretization of State-Constrained Elliptic Optimal Control Problems with Semilinear State Equation

SIAM Journal on Control and Optimization ◽

10.1137/140960645 ◽

2015 ◽

Vol 53 (2) ◽

pp. 874-904 ◽

Cited By ~ 14

Author(s):

Ira Neitzel ◽

Johannes Pfefferer ◽

Arnd Rösch

Keyword(s):

Optimal Control ◽

Finite Element ◽

Optimal Control Problems ◽

State Equation ◽

Control Problems ◽

Finite Element Discretization ◽

Element Discretization ◽

Elliptic Optimal Control Problems ◽

Elliptic Optimal Control

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