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We consider the Navier-Stokes system in a bounded domain with a smooth boundary. Given a sufficiently regular time-dependent global solution, we construct a finite-dimensional feedback control that is supported by a given open set and…

Optimization and Control · Mathematics 2010-09-20 Viorel Barbu , Sergio S. Rodrigues , Armen Shirikyan

We develop a variational multiscale proper orthogonal decomposition reduced-order model for turbulent incompressible Navier-Stokes equations. The error analysis of the full discretization of the model is presented. All error contributions…

Numerical Analysis · Mathematics 2013-06-03 Traian Iliescu , Zhu Wang

We propose an a posteriori error estimator for a sparse optimal control problem: the control variable lies in the space of regular Borel measures. We consider a solution technique that relies on the discretization of the control variable as…

Numerical Analysis · Mathematics 2018-06-14 Francisco Fuica , Enrique Otarola , Abner J. Salgado

This work discusses the finite element discretization of an optimal control problem for the linear wave equation with time-dependent controls of bounded variation. The main focus lies on the convergence analysis of the discretization…

Optimization and Control · Mathematics 2019-07-26 Sebastian Engel , Philip Trautmann , Boris Vexler

This article presents a general and novel approach to the automation of goal-oriented error control in the solution of nonlinear stationary finite element variational problems. The approach is based on automated linearization to obtain the…

Numerical Analysis · Mathematics 2012-05-01 Marie E. Rognes , Anders Logg

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

In this paper we study a distributed optimal control problem for a three-dimensional Navier-Stokes-$\alpha$ model. We prove the solvability of the optimal control problem, and derive first-order optimality conditions by using a Lagrange…

Optimization and Control · Mathematics 2019-05-07 Exequiel Mallea-Zepeda , Elva Ortega-Torres , Élder J. Villamizar-Roa

We devise an a posteriori error estimator for an affine optimal control problem subject to a semilinear elliptic PDE and control constraints. To approximate the problem, we consider a semidiscrete scheme based on the variational…

Optimization and Control · Mathematics 2025-05-08 Francisco Fuica , Nicolai Jork

We derive a posteriori error estimators for an optimal control problem governed by a convection-reaction-diffusion equation; control constraints are also considered. We consider a family of low-order stabilized finite element methods to…

Numerical Analysis · Mathematics 2017-04-24 Alejandro Allendes , Enrique Otarola , Richard Rankin

This paper studies an optimal control problem governed by a semilinear elliptic equation, in which the control acts in a multiplicative or bilinear way as the reaction coefficient of the equation. We focus on the numerical discretization of…

Optimization and Control · Mathematics 2025-06-25 Eduardo Casas , Konstantinos Chrysafinos , Mariano Mateos

We analyze, in two dimensions, an optimal control problem for the Navier--Stokes equations where the control variable corresponds to the amplitude of forces modeled as point sources; control constraints are also considered. This particular…

Optimization and Control · Mathematics 2022-08-19 Francisco Fuica , Felipe Lepe , Enrique Otarola , Daniel Quero

Variational approaches have been used successfully as a strategy to take advantage from real data measurements. In several applications, this approach gives a means to increase the accuracy of numerical simulations. In the particular case…

Optimization and Control · Mathematics 2015-10-15 Telma Guerra , Adélia Sequeira , Jorge Tiago

In this work we study an optimal control problem subject to the instationary Navier-Stokes equations, where the control enters via an inhomogeneous Neumann/Do-Nothing boundary condition. Despite the Navier-Stokes equations with these…

Optimization and Control · Mathematics 2026-05-20 Boris Vexler , Jakob Wagner

This work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function. It concerns Symplectic Euler solutions of the Hamiltonian…

Optimization and Control · Mathematics 2016-02-23 Jesper Karlsson , Stig Larsson , Mattias Sandberg , Anders Szepessy , Raùl Tempone

A first-order linear fully discrete scheme is studied for the incompressible time-dependent Navier-Stokes equations in three-dimensional domains. This scheme, based on an incremental pressure projection method, decouples each component of…

Numerical Analysis · Mathematics 2014-11-27 F. Guillén-González , M. V. Redondo-Neble

We consider the variational discretization of a linear-quadratic optimal control problem with pointwise control and state constraints. In order to allow for a Fr\'echet smooth norm, the problem is reformulated by means of a reflexive…

Optimization and Control · Mathematics 2010-08-24 Morten Vierling

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 consider a control-constrained parabolic optimal control problem without Tikhonov term in the tracking functional. For the numerical treatment, we use variational discretization of its Tikhonov regularization: For the state and the…

Optimization and Control · Mathematics 2017-12-08 Nikolaus von Daniels , Michael Hinze

We design and analyze solution techniques for a linear-quadratic optimal control problem involving the integral fractional Laplacian. We derive existence and uniqueness results, first order optimality conditions, and regularity estimates…

Optimization and Control · Mathematics 2020-10-09 Marta D'Elia , Christian Glusa , Enrique Otarola

We consider a velocity tracking problem for stochastic Navier-Stokes equations in a 2D-bounded domain. The control acts on the boundary through an injection-suction device with uncertainty, which acts in accordance with the non-homogeneous…

Probability · Mathematics 2024-09-04 Nikolai Chemetov , Fernanda Cipriano