English
Related papers

Related papers: Robust space-time finite element error estimates f…

200 papers

In this paper we study the mixed virtual element approximation to an elliptic optimal control problem with boundary observations. The objective functional of this type of optimal control problem contains the outward normal derivatives of…

Numerical Analysis · Mathematics 2023-12-19 Minghui Yang , Zhaojie Zhou

In this paper, we study a time optimal internal control problem governed by the heat equation in $\Omega\times [0,\infty)$. In the problem, the target set $S$ is nonempty in $L^2(\Omega)$, the control set $U$ is closed, bounded and nonempty…

Optimization and Control · Mathematics 2007-05-23 Gengsheng Wang

This paper is concerned with the recovery of (approximate) solutions to parabolic problems from incomplete and possibly inconsistent observational data, given on a time-space cylinder that is a strict subset of the computational domain…

Numerical Analysis · Mathematics 2021-07-13 Wolfgang Dahmen , Rob Stevenson , Jan Westerdiep

In this paper, a quadratic optimal control problem is considered for second-order parabolic PDEs with homogeneous Dirichlet boundary conditions, in which the "point" control function (depending only on time) constitutes a source term. These…

Systems and Control · Electrical Eng. & Systems 2024-07-04 Gilberto O. Corrêa , Marlon M. López-Flores , Alexandre L. Madureira

We investigate $C^1$ finite element methods for one dimensional elliptic distributed optimal control problems with pointwise constraints on the derivative of the state formulated as fourth order variational inequalities for the state…

Numerical Analysis · Mathematics 2020-06-29 Susanne C. Brenner , Li-Yeng Sung , Winnifried Wollner

Tikhonov regularization is one of the most commonly used methods of regularization of ill-posed problems. In the setting of finite element solutions of elliptic partial differential control problems, Tikhonov regularization amounts to…

Numerical Analysis · Mathematics 2016-09-19 Erik Burman , Peter Hansbo , Mats Larson

We first give a general error estimate for the nonconforming approximation of a problem for which a Banach-Ne{\v c}as-Babu{\v s}ka (BNB) inequality holds. This framework covers parabolic problems with general conditions in time (initial…

Numerical Analysis · Mathematics 2023-04-24 Wolfgang Arendt , Isabelle Chalendar , Robert Eymard

We study a finite-element based space-time discretisation for the 2D stochastic Navier-Stokes equations in a bounded domain supplemented with no-slip boundary conditions. We prove optimal convergence rates in the energy norm with respect to…

Numerical Analysis · Mathematics 2022-10-06 Dominic Breit , Andreas Prohl

Infinite horizon open loop optimal control problems for semilinear parabolic equations are investigated. The controls are subject to a cost-functional which promotes sparsity in time. The focus is put on deriving first order optimality…

Optimization and Control · Mathematics 2021-12-14 Eduardo Casas , Karl Kunisch

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

The aim of this paper is to extend the global error estimation and control addressed in Lang and Verwer [SIAM J. Sci. Comput. 29, 2007] for initial value problems to finite difference solutions of semilinear parabolic partial differential…

Numerical Analysis · Mathematics 2018-02-16 Kristian Debrabant , Jens Lang

We study problems of optimal boundary control with systems governed by linear hyperbolic partial differential equations. The objective function is quadratic and given by an integral over the finite time interval $(0,\, T)$ that depends on…

Analysis of PDEs · Mathematics 2018-11-08 Martin Gugat , Falk Hante

The study is devoted to mathematical modeling and optimal control design of longitudinal motions of a rectilinear elastic rod. The control inputs are a force, which is normal to the cross section and distributed piecewise constantly along…

Optimization and Control · Mathematics 2022-07-22 Georgy Kostin , Alexander Gavrikov

This paper presents the design and analysis of a Hybrid High-Order (HHO) approximation for a distributed optimal control problem governed by the Poisson equation. We propose three distinct schemes to address unconstrained control problems…

Numerical Analysis · Mathematics 2025-01-14 Gouranga Mallik , Ramesh Chandra Sau

The purpose of this work is the design and analysis of a reliable and efficient a posteriori error estimator for the so-called pointwise tracking optimal control problem. This linear-quadratic optimal control problem entails the…

Numerical Analysis · Mathematics 2016-08-30 Alejandro Allendes , Enrique Otarola , Richard Rankin , Abner J. Salgado

The main aim of this article is to analyze mixed finite element method for the second order Dirichlet boundary control problem. Therein, we develop both a priori and a posteriori error analysis using the energy space based approach. We…

Numerical Analysis · Mathematics 2022-07-22 Divay Garg , Kamana Porwal

The purpose of this work is the formulation of optimality conditions for phase-field optimal control problems. The forward problem is first stated as an abstract nonlinear optimization problem, and then the necessary optimality conditions…

Optimization and Control · Mathematics 2023-10-06 Denis Khimin , Johannes Lankeit , Marc C. Steinbach , Thomas Wick

This paper concerns some time optimal control problems of three different ordinary differential equations in $\mathbb{R}^2$. Corresponding to certain initial data and controls, the solutions of the systems quench at finite time. The goal to…

Optimization and Control · Mathematics 2012-09-06 Ping Lin

In this paper, problems of optimal control are considered where in the objective function, in addition to the control cost there is a tracking term that measures the distance to a desired stationary state. The tracking term is given by some…

Optimization and Control · Mathematics 2020-06-15 Martin Gugat , Michael Schuster , Enrique Zuazua

This paper discusses the energy optimal control problem for the class of quantum systems that possess dynamical symmetry of SU(1,1), which are widely studied in various physical problems in the quantum theory. Based on the maximum principle…

Optimization and Control · Mathematics 2007-09-13 Jian-Wu Wu , Chun-Wen Li , Jing Zhang , Tzyh-Jong Tarn