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The optimal control of problems that are constrained by partial differential equations with uncertainties and with uncertain controls is addressed. The Lagrangian that defines the problem is postulated in terms of stochastic functions, with…

Optimization and Control · Mathematics 2012-11-19 Eveline Rosseel , Garth N. Wells

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

In this work, we consider optimal control problems for mechanical systems on vector spaces with fixed initial and free final state and a quadratic Lagrange term. Specifically, the dynamics is described by a second order ODE containing an…

We consider finite element solutions to optimization problems, where the state depends on the possibly constrained control through a linear partial differential equation. Basing upon a reduced and rescaled optimality system, we derive a…

Numerical Analysis · Mathematics 2025-03-18 Fernando Gaspoz , Christian Kreuzer , Andreas Veeser , Winnifried Wollner

We prove a sufficient optimality condition for non-linear optimal control problems with delays in both state and control variables. Our result requires the verification of a Hamilton-Jacobi partial differential equation and is obtained…

Optimization and Control · Mathematics 2019-06-17 Ana P. Lemos-Paiao , Cristiana J. Silva , Delfim F. M. Torres

We propose and analyze a general framework for space-time finite element methods that is based on least-squares finite element methods for solving a first-order reformulation of the thick parabolic obstacle problem. Discretizations based on…

Numerical Analysis · Mathematics 2025-03-12 José Joaquín Carvajal , Davood Damircheli , Thomas Führer , Francisco Fuica , Michael Karkulik

Using the recent weighted generalized fractional order operators of Hattaf, a general fractional optimal control problem without constraints on the values of the control functions is formulated and a corresponding (weak) version of…

Optimization and Control · Mathematics 2023-12-19 Houssine Zine , El Mehdi Lotfi , Delfim F. M. Torres , Noura Yousfi

Solving parabolic optimal control problems can be inherently challenging in the field of science and engineering, especially with constraints on the nonsmooth distributed control. Motivated by the extensive applicability of the alternating…

Optimization and Control · Mathematics 2026-03-03 Haiming Song , Jinda Yang , Yuran Yang , Jianhua Yuan

In this paper, we study the numerical approximation of a system of PDEs with fractional time derivatives. This system is derived from an optimal control problem for a time-fractional Fokker-Planck equation with time dependent drift by…

Numerical Analysis · Mathematics 2020-06-08 Fabio Camilli , Serikbolsyn Duisembay , Qing Tang

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

In this paper, we present a method that enables solving in parallel the Euler-Lagrange system associated with the optimal control of a parabolic equation. Our approach is based on an iterative update of a sequence of intermediate targets…

Optimization and Control · Mathematics 2012-03-13 Yvon Maday , Mohamed-Kamel Riahi , Julien Salomon

This paper investigates a space-time interface-fitted approximation of a moving-interface optimal control problem with energy regularization. We reformulate the optimality conditions into a variational problem involving both the state and…

Optimization and Control · Mathematics 2025-06-13 Quang Huy Nguyen , Phuong Cuc Hoang , Van Chien Le , Thi Thanh Mai Ta

In this work, we present a second-order numerical scheme to address the solution of optimal control problems constrained by the evolution of nonlinear Fokker-Planck equations arising from socio-economic dynamics. In order to design an…

Numerical Analysis · Mathematics 2025-10-20 Giacomo Albi , Elisa Calzola

The purpose of this work is the development of space-time discretization schemes for phase-field optimal control problems. First, a time discretization of the forward problem is derived using a discontinuous Galerkin formulation. Here, a…

Optimization and Control · Mathematics 2022-03-24 Denis Khimin , Marc C. Steinbach , Thomas Wick

We tackle a nonlinear optimal control problem for a stochastic differential equation in Euclidean space and its state-linear counterpart for the Fokker-Planck-Kolmogorov equation in the space of probabilities. Our approach is founded on a…

Optimization and Control · Mathematics 2024-09-23 Roman Chertovskih , Nikolay Pogodaev , Maxim Staritsyn , A. Pedro Aguiar

In this paper, we investigate optimal control problems governed by the parabolic interface equation, in which the control acts on the interface. The solution to this problem exhibits low global regularity due to the jump of the coefficient…

Numerical Analysis · Mathematics 2025-10-15 Xindan Zhang , Jianping Zhao , Yanren Hou

We consider a linear-quadratic pde constrained optimal control problem on an evolving surface with pointwise state constraints. We reformulate the optimization problem on a fixed surface and approximate the reformulated problem by a…

Optimization and Control · Mathematics 2016-04-27 Michael Hinze , Heiko Kröner

We consider space-time tracking type distributed optimal control problems for the wave equation in the space-time domain $Q:= \Omega \times (0,T) \subset {\mathbb{R}}^{n+1}$, where the control is assumed to be in the energy space…

Numerical Analysis · Mathematics 2022-11-07 Richard Löscher , Olaf Steinbach

The paper is concerned with space-time IgA approximations of parabolic initial-boundary value problems. We deduce guaranteed and fully computable error bounds adapted to special features of IgA approximations and investigate their…

Numerical Analysis · Mathematics 2018-02-20 Ulrich Langer , Svetlana Matculevich , Sergey Repin

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
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