English
Related papers

Related papers: Adaptive finite element methods for an optimal con…

200 papers

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

In this paper we consider a parabolic optimal control problem with a Dirac type control with moving point source in two space dimensions. We discretize the problem with piecewise constant functions in time and continuous piecewise linear…

Numerical Analysis · Mathematics 2018-08-17 Dmitriy Leykekhman , Boris Vexler

In this paper we consider the convergence analysis of adaptive finite element method for elliptic optimal control problems with pointwise control constraints. We use variational discretization concept to discretize the control variable and…

Numerical Analysis · Mathematics 2016-08-31 Wei Gong , Ningning Yan

This article discusses numerical analysis of the distributed optimal control problem governed by the von K\'{a}rm\'{a}n equations defined on a polygonal domain in $\mathbb{R}^2$. The state and adjoint variables are discretised using the…

Numerical Analysis · Mathematics 2021-07-14 Sudipto Chowdhury , Asha K. Dond , Neela Nataraj , Devika Shylaja

We consider an elliptic linear-quadratic parameter estimation problem with a finite number of parameters. A novel a priori bound for the parameter error is proved and, based on this bound, an adaptive finite element method driven by an a…

Numerical Analysis · Mathematics 2022-09-05 Roland Becker , Michael Innerberger , Dirk Praetorius

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

In this work, an adaptive edge element method is developed for an H(curl)-elliptic constrained optimal control problem. We use the lowest-order Nedelec's edge elements of first family and the piecewise (element-wise) constant functions to…

Numerical Analysis · Mathematics 2021-06-30 Bowen Li , Jun Zou

We consider a linear-quadratic elliptic optimal control problem with point evaluations of the state variable in the cost functional. The state variable is discretized by conforming linear finite elements. For control discretization, three…

Numerical Analysis · Mathematics 2018-02-09 Niklas Behringer , Dominik Meidner , Boris Vexler

In this article, we derive \textit{a posteriori} error estimates for the Dirichlet boundary control problem governed by Stokes equation. An energy-based method has been deployed to solve the Dirichlet boundary control problem. We employ an…

Numerical Analysis · Mathematics 2024-01-30 Thirupathi Gudi , Ramesh Chandra Sau

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

In two and three dimensional Lipschitz, but not necessarily convex, polytopal domains, we propose and analyze a posteriori error estimators for an optimal control problem involving the stationary Navier--Stokes equations; control…

Numerical Analysis · Mathematics 2021-01-13 Alejandro Allendes , Francisco Fuica , Enrique Otarola , Daniel Quero

We consider Poisson's equation with a finite number of weighted Dirac masses as a source term, together with its discretization by means of conforming finite elements. For the error in fractional Sobolev spaces, we propose residual-type a…

Numerical Analysis · Mathematics 2015-07-30 Fernando D. Gaspoz , Pedro Morin , Andreas Veeser

In this paper, we develop a new residual-based pointwise a posteriori error estimator of the quadratic finite element method for the Signorini problem. The supremum norm a posteriori error estimates enable us to locate the singularities…

Numerical Analysis · Mathematics 2024-01-05 Rohit Khandelwal , Kamana Porwal , Tanvi Wadhawan

This paper focuses on a posteriori error estimates for a pressure-robust finite element method, which incorporates a divergence-free reconstruction operator, within the context of the distributed optimal control problem constrained by the…

Numerical Analysis · Mathematics 2026-01-30 Jingshi Li , Jiachuan Zhang

This work reviews goal-oriented a posteriori error control, adaptivity and solver control for finite element approximations to boundary and initial-boundary value problems for stationary and non-stationary partial differential equations,…

Numerical Analysis · Mathematics 2024-12-02 Bernhard Endtmayer , Ulrich Langer , Thomas Richter , Andreas Schafelner , Thomas Wick

The convergence of an adaptive mixed finite element method for general second order linear elliptic problems defined on simply connected bounded polygonal domains is analyzed in this paper. The main difficulties in the analysis are posed by…

Numerical Analysis · Mathematics 2014-02-14 Asha K. Dond , Neela Nataraj , Amiya K. Pani

In this paper, we consider the integrating factor midpoint method for wave-type equations and derive optimal order a posteriori error estimates. We first introduce an integrating factor midpoint approximation defined by the piecewise linear…

Numerical Analysis · Mathematics 2026-03-03 Xianfa Hu , Fazhan Geng , Wansheng Wang

The numerical approximation of convection-dominated problems continues to remain subject of strong interest. Families of stabilization techniques for finite element methods were developed in the past. Adaptive techniques based on a…

Numerical Analysis · Mathematics 2018-03-20 Kristina Schwegler , Marius P. Bruchhäuser , Markus Bause

We propose and analyze a posteriori error estimates for a control-constrained optimal control problem with bang-bang solutions. We consider a solution strategy based on the variational approach, where the control variable is not…

Optimization and Control · Mathematics 2025-05-26 Francisco Fuica

In this paper, we investigate an optimal control problem governed by parabolic equations with measure-valued controls over time. We establish the well-posedness of the optimal control problem and derive the first-order optimality condition…

Optimization and Control · Mathematics 2024-04-04 Wei Gong , Dongdong Liang