A priori error analysis for finite element approximation of parabolic optimal control problems with pointwise control

W Gong, M Hinze, Z Zhou - SIAM Journal on Control and Optimization, 2014 - SIAM
We consider finite element approximations of parabolic control problems with pointwise
control. The state equation exhibits low regularity due to the control imposed pointwisely; …

Strong rates of convergence for a space-time discretization of the backward stochastic heat equation, and of a linear-quadratic control problem for the stochastic heat …

A Prohl, Y Wang - ESAIM: Control, Optimisation and Calculus of …, 2021 - esaim-cocv.org
We verify strong rates of convergence for a time-implicit, finite-element based space-time
discretization of the backward stochastic heat equation, and the forward-backward …

Space-time finite element approximation of parabolic optimal control problems

W Gong, M Hinze, ZJ Zhou - Journal of Numerical Mathematics, 2012 - degruyter.com
In this paper we investigate a space-time finite element approximation of parabolic optimal
control problems. The first order optimality conditions are transformed into an elliptic …

Error estimates for finite element approximations of parabolic equations with measure data

W Gong - Mathematics of computation, 2013 - ams.org
In this paper we study the a priori error estimates for the finite element approximations of
parabolic equations with measure data, especially we consider problems with separate …

New regularity results and finite element error estimates for a class of parabolic optimal control problems with pointwise state constraints

C Christof, B Vexler - ESAIM: Control, Optimisation and Calculus of …, 2021 - esaim-cocv.org
We study first-order necessary optimality conditions and finite element error estimates for a
class of distributed parabolic optimal control problems with pointwise state constraints. It is …

Finite Element Error Estimation for Parabolic Optimal Control Problems with Time Delay

X Zhang, J Zhao, Y Hou - Applied Numerical Mathematics, 2025 - Elsevier
In this paper, we develop a priori error estimates for the finite element approximations of
parabolic optimal control problems with time delay and pointwise control constraints. At first …

An iterative proper orthogonal decomposition method for a parabolic optimal control problem

L Huang, H Zhao, T Sun - Journal of Applied Mathematics and Computing, 2024 - Springer
An iterative proper orthogonal decomposition (POD) method for a parabolic optimal control
problem is investigated in this paper. Firstly, we construct the finite element method, where …

[HTML][HTML] Принцип максимума Понтрягина в задаче оптимального управления уравнением теплопроводности при наличии смешанных ограничений

ДВ Сугак - Международный научно-исследовательский журнал, 2023 - cyberleninka.ru
В статье исследуется задача оптимального управления системой дифференциальных
уравнений в частных производных параболического типа второго порядка в случае …

A new finite element method for elliptic optimal control problems with pointwise state constraints in energy spaces

W Gong, Z Tan - Journal of Scientific Computing, 2025 - Springer
In this paper we propose a new finite element method for solving elliptic optimal control
problems with pointwise state constraints, including the distributed controls and the Dirichlet …

[КНИГА][B] A-posteriori error estimation of discrete POD models for PDE-constrained optimal control

M Gubisch, I Neitzel, S Volkwein - 2017 - Springer
In this work a-posteriori error estimates for linear-quadratic optimal control problems
governed by parabolic equations are considered. Different error estimation techniques for …