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This work addresses an optimal control problem constrained by a degenerate kinetic equation of parabolic-hyperbolic type. Using a hypocoercivity framework we establish the well-posedness of the problem and demonstrate that the optimal…

Numerical Analysis · Mathematics 2024-12-17 Aaron Pim , Tristan Pryer , Alex Trenam

An optimal control problem driven by an ordinary differential equation under continuous state constraints is considered in this study. From an operational point of view, we introduce a discrete state constraints optimal control problem and…

Optimization and Control · Mathematics 2018-12-04 Shuzhen Yang

This paper aims to study the convergence of adaptive finite element method for control constrained elliptic optimal control problems under $L^2$-norm. We prove the contraction property and quasi-optimal complexity for the $L^2$-norm errors…

Numerical Analysis · Mathematics 2016-11-16 Wei Gong , Ningning Yan , Zhaojie Zhou

We consider linear model reduction in both the control and state variables for unconstrained linear-quadratic optimal control problems subject to time-varying parabolic PDEs. The first-order optimality condition for a state-space reduced…

Optimization and Control · Mathematics 2025-10-17 Michael Kartmann , Stefan Volkwein

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 or Neumann boundary controls. The main idea is to use…

Numerical Analysis · Mathematics 2023-06-07 Wei Gong , Zhiyu Tan

We consider the finite element discretization and the iterative solution of singularly perturbed elliptic reaction-diffusion equations in three-dimensional computational domains. These equations arise from the optimality conditions for…

Numerical Analysis · Mathematics 2021-02-09 Ulrich Langer , Olaf Steinbach , Huidong Yang

We shall develop a fully discrete space-time adaptive method for linear parabolic problems based on new reliable and efficient a posteriori analysis for higher order dG(s) finite element discretisations. The adaptive strategy is motivated…

Numerical Analysis · Mathematics 2016-10-24 Fernando Gaspoz , Christian Kreuzer , Kunibert Siebert , Daniel Ziegler

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 propose and analyze an a posteriori error estimator for a PDE-constrained optimization problem involving a nondifferentiable cost functional, fractional diffusion, and control-constraints. We realize fractional diffusion as the…

Numerical Analysis · Mathematics 2019-06-04 Enrique Otarola

We study a linear-quadratic optimal control problem involving a parabolic equation with fractional diffusion and Caputo fractional time derivative of orders $s \in (0,1)$ and $\gamma \in (0,1]$, respectively. The spatial fractional…

Optimization and Control · Mathematics 2015-04-02 Harbir Antil , Enrique Otarola , Abner J. Salgado

We propose and analyze reliable and efficient a posteriori error estimators for an optimal control problem that involves a nondifferentiable cost functional, the Poisson problem as state equation and control constraints. To approximate the…

Numerical Analysis · Mathematics 2019-01-14 Alejandro Allendes , Francisco Fuica , Enrique Otárola

We derive globally reliable a posteriori error estimators for a PDE-constrained optimization problem involving linear models in fluid dynamics as state equation; control constraints are also considered. The corresponding local error…

Numerical Analysis · Mathematics 2017-08-03 Alejandro Allendes , Enrique Otarola , Richard Rankin

Optimization problems with $L^1$-control cost functional subject to an elliptic partial differential equation (PDE) are considered. However, different from the finite dimensional $l^1$-regularization optimization, the resulting discretized…

Optimization and Control · Mathematics 2017-09-28 Xiaoliang Song , Bo Chen , Bo Yu

In this paper we present and analyze a weighted residual a posteriori error estimate for an optimal control problem. The problem involves a nondifferentiable cost functional, a state equation with an integral fractional Laplacian, and…

Numerical Analysis · Mathematics 2023-09-18 Fangyuan Wang , Qiming Wang , Zhaojie Zhou

This paper is concerned with finite element error estimates for Neumann boundary control problems posed on convex and polyhedral domains. Different discretization concepts are considered and for each optimal discretization error estimates…

Numerical Analysis · Mathematics 2024-09-18 Johannes Pfefferer , Boris Vexler

In this paper, an abstract framework for the error analysis of discontinuous finite element method is developed for the distributed and Neumann boundary control problems governed by the stationary Stokes equation with control constraints.…

Numerical Analysis · Mathematics 2021-11-01 Asha K Dond , Thirupathi Gudi , Ramesh Ch. Sau

We consider a space-time finite element method for the numerical solution of a distributed tracking-type optimal control problem subject to the heat equation with state constraints. The cost or regularization term is formulated in an…

Numerical Analysis · Mathematics 2024-10-10 Richard Löscher , Michael Reichelt , Olaf Steinbach

The paper presents the first rigorous error analysis of an unfitted finite element method for a linear parabolic problem posed on an evolving domain $\Omega(t)$ that may undergo a topological change, such as, for example, a domain…

Numerical Analysis · Mathematics 2026-01-28 Maxim A. Olshanskii , Arnold Reusken

This study presents an aposteriori error analysis of adaptive finite element approximations of parabolic boundary control problems with bilateral box constraints that act on a Neumann boundary. The control problem is discretized using the…

Numerical Analysis · Mathematics 2025-07-22 Ram Manohar , B. V. Rathish Kumar , Kedarnath Buda , Rajen Kumar Sinha

We derive error estimates for a linear-quadratic elliptic distributed optimal control problem with pointwise control constraints that can be applied to standard finite element methods and multiscale finite element methods.

Optimization and Control · Mathematics 2024-10-08 Susanne C. Brenner , Li-yeng Sung
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