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Space-time finite element discretizations of time-optimal control problems governed by linear parabolic PDEs and subject to pointwise control constraints are considered. Optimal a priori error estimates are obtained for the control variable…

Optimization and Control · Mathematics 2018-09-14 Lucas Bonifacius , Konstantin Pieper , Boris Vexler

We investigate the application of a posteriori error estimates to a fractional optimal control problem with pointwise control constraints. Specifically, we address a problem in which the state equation is formulated as an integral form of…

Optimization and Control · Mathematics 2023-10-10 Fangyuan Wang , Qiming Wang , Zhaojie Zhou

We derive a-priori error estimates for the finite-element approximation of a distributed optimal control problem governed by the steady one-dimensional Burgers equation with pointwise box constraints on the control. Here the approximation…

Optimization and Control · Mathematics 2014-11-18 Pedro Martín Merino Rosero

This work presents a convex-optimization-based framework for analysis and control of nonlinear partial differential equations. The approach uses a particular weak embedding of the nonlinear PDE, resulting in a linear equation in the space…

Optimization and Control · Mathematics 2018-04-23 Milan Korda , Didier Henrion , Jean-Bernard Lasserre

This paper is concerned with the discretization error analysis of semilinear Neumann boundary control problems in polygonal domains with pointwise inequality constraints on the control. The approximations of the control are piecewise…

Numerical Analysis · Mathematics 2015-05-12 Johannes Pfefferer , Klaus Krumbiegel

This article studies a priori error analysis for linear parabolic interface problems with measure data in time in a bounded convex polygonal domain in $\mathbb{R}^2$. We have used the standard continuous fitted finite element discretization…

Numerical Analysis · Mathematics 2021-12-03 Jhuma Sen Gupta

In this paper, we consider a class of time-optimal control problems governed by linear parabolic equations with mixed control-state constraints and end-point constraints, and without Tikhonov regularization term in the objective function.…

Optimization and Control · Mathematics 2025-09-04 Huynh Khanh , Bui Trong Kien

We consider a control-constrained optimal control problem subject to time-harmonic Maxwell's equations; the control variable belongs to a finite-dimensional set and enters the state equation as a coefficient. We derive existence of optimal…

Numerical Analysis · Mathematics 2024-05-10 Francisco Fuica , Felipe Lepe , Pablo Venegas

We consider an optimal control problem on a bounded domain $\Omega\subset\mathbb{R}^2,$ governed by a parabolic convection--diffusion--reaction equation with pointwise control constraints. We follow the optimize--then--discretize approach,…

Numerical Analysis · Mathematics 2025-12-11 Christos Pervolianakis

Optimal control of the singular nonlinear parabolic PDE which is a distributional formulation of multidimensional and multiphase Stefan-type free boundary problem is analyzed. Approximating sequence of finite-dimensional optimal control…

Analysis of PDEs · Mathematics 2020-06-16 Ugur G. Abdulla , Evan Cosgrove

This work presents and analyzes space-time finite element methods on fully unstructured simplicial space-time meshes for the numerical solution of parabolic optimal control problems. Using Babu\v{s}ka's theorem, we show well-posedness of…

Numerical Analysis · Mathematics 2020-04-07 Ulrich Langer , Olaf Steinbach , Fredi Tröltzsch , Huidong Yang

We consider finite element solutions to quadratic optimization problems, where the state depends on the control via a well-posed linear partial differential equation. Exploiting the structure of a suitably reduced optimality system, we…

Numerical Analysis · Mathematics 2019-10-03 Fernando Gaspoz , Christian Kreuzer , Andreas Veeser , Winnifried Wollner

The article examines a linear-quadratic Neumann control problem that is governed by a non-coercive elliptic equation. Due to the non-self-adjoint nature of the linear control-to-state operator, it is necessary to independently study both…

Optimization and Control · Mathematics 2025-06-25 Thomas Apel , Mariano Mateos , Arnd Rösch

In this article a special class of nonlinear optimal control problems involving a bilinear term in the boundary condition is studied. These kind of problems arise for instance in the identification of an unknown space-dependent Robin…

Numerical Analysis · Mathematics 2024-12-20 Max Winkler

We consider a distributed optimal control problem subject to a parabolic evolution equation as constraint. The control will be considered in the energy norm of the anisotropic Sobolev space $[H_{0;,0}^{1,1/2}(Q)]^\ast$, such that the state…

Numerical Analysis · Mathematics 2025-02-14 Richard Löscher , Michael Reichelt , Olaf Steinbach

In this paper we discuss the numerical solution of elliptic distributed optimal control problems with state or control constraints when the control is considered in the energy norm. As in the unconstrained case we can relate the…

Numerical Analysis · Mathematics 2023-06-28 Peter Gangl , Richard Löscher , Olaf Steinbach

In this paper, we carry out the numerical analysis of a nonsmooth quasilinear elliptic optimal control problem, where the coefficient in the divergence term of the corresponding state equation is not differentiable with respect to the state…

Numerical Analysis · Mathematics 2024-02-23 Christian Clason , Vu Huu Nhu , Arnd Rösch

This paper studies a kind of minimal time control problems related to the exact synchronization for a controlled linear system of parabolic equations. Each problem depends on two parameters: the bound of controls and the initial state. The…

Optimization and Control · Mathematics 2018-03-02 Lijuan Wang , Qishu Yan

We analyze space-time finite element methods for the numerical solution of distributed parabolic optimal control problems with energy regularization in the Bochner space $L^2(0,T;H^{-1}(\Omega))$. By duality, the related norm can be…

Numerical Analysis · Mathematics 2020-04-22 Ulrich Langer , Olaf Steinbach , Fredi Tröltzsch , Huidong Yang

This work concentrates on a class of optimal control problems for semilinear parabolic equations subject to control constraint of the form $\|u(t)\|_{L^1(\Omega)} \le \gamma$ for $t \in (0,T)$. This limits the total control that can be…

Optimization and Control · Mathematics 2021-12-03 Eduardo Casas , Karl Kunisch