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We study the numerical approximation of linear-quadratic optimal control problems subject to the fractional Laplace equation with its spectral definition. We compute an approximation of the state equation using a discretization of the…

Numerical Analysis · Mathematics 2018-09-28 Stefan Dohr , Christian Kahle , Sergejs Rogovs , Piotr Swierczynski

We consider standard tracking-type, distributed elliptic optimal control problems with $L^2$ regularization, and their finite element discretization. We are investigating the $L^2$ error between the finite element approximation $u_{\varrho…

Numerical Analysis · Mathematics 2022-07-12 Ulrich Langer , Richard Löscher , Olaf Steinbach , Huidong Yang

In [1] we consider an optimal control problem subject to a semilinear elliptic PDE together with its variational discretization, where we provide a condition which allows to decide whether a solution of the necessary first order conditions…

Optimization and Control · Mathematics 2017-05-04 Ahmad Ahmad Ali , Klaus Deckelnick , Michael Hinze

We discretize a risk-neutral optimal control problem governed by a linear elliptic partial differential equation with random inputs using a Monte Carlo sample-based approximation and a finite element discretization, yielding finite…

Optimization and Control · Mathematics 2023-11-10 Johannes Milz

Finite element methods for a model elliptic distributed optimal control problem with pointwise state constraints are considered from the perspective of fourth order boundary value problems.

Numerical Analysis · Mathematics 2020-08-20 Susanne C. Brenner

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 adopt the integral definition of the fractional Laplace operator and analyze solution techniques for fractional, semilinear, and elliptic optimal control problems posed on Lipschitz polytopes. We consider two strategies of…

Numerical Analysis · Mathematics 2023-03-02 Enrique Otarola

This paper develops and analyses numerical approximation for linear-quadratic optimal control problem governed by elliptic interface equations. We adopt variational discretization concept to discretize optimal control problem, and apply an…

Numerical Analysis · Mathematics 2018-06-04 Chao Chao Yang , Tao Wang , Xiaoping Xie

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

We consider some boundary value tracking optimal control problem constrained by a Neumann boundary value problem for some elliptic partial differential equation where the control acts as right-hand side. This optimal control problem can be…

Numerical Analysis · Mathematics 2026-03-12 Ulrich Langer , Richard Löscher , Olaf Steinbach , Huidong Yang

The aim of this work is to derive a priori error estimates for finite element discretizations of control--constrained optimal control problems that involve the Stokes system and Dirac measures. The first problem entails the minimization of…

Numerical Analysis · Mathematics 2020-04-29 Francisco Fuica , Enrique Otarola , Daniel Quero

In this paper, we carry out the numerical analysis of a nonsmooth quasilinear elliptic optimal control problem, where the coefficient in the divergence term of the corresponding state equation is not differentiable with respect to the state…

Numerical Analysis · Mathematics 2024-02-23 Christian Clason , Vu Huu Nhu , Arnd Rösch

We propose and analyze a posteriori error estimators for an optimal control problem that involves an elliptic partial differential equation as state equation and a control variable that enters the state equation as a coefficient; pointwise…

Optimization and Control · Mathematics 2022-03-31 Francisco Fuica , Enrique Otarola

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 construct and analyze a multiscale finite element method for an elliptic distributed optimal control problem with pointwise control constraints, where the state equation has rough coefficients. We show that the performance of the…

Numerical Analysis · Mathematics 2023-09-29 Susanne C. Brenner , Jose C. Garay , Li-yeng Sung

We adopt the integral definition of the fractional Laplace operator and analyze an optimal control problem for a fractional semilinear elliptic partial differential equation (PDE); control constraints are also considered. We establish the…

Numerical Analysis · Mathematics 2021-09-07 Enrique Otarola

In this paper we consider some optimal control problems governed by elliptic partial differential equations. The solution is the state variable, while the control variable is, depending on the case, the coefficient of the PDE, the…

Optimization and Control · Mathematics 2026-01-06 Giuseppe Buttazzo , Juan Casado-Díaz , Faustino Maestre

We adopt the integral definition of the fractional Laplace operator and study an optimal control problem on Lipschitz domains that involves a fractional elliptic partial differential equation (PDE) as state equation and a control variable…

Numerical Analysis · Mathematics 2024-02-14 Francisco Bersetche , Francisco Fuica , Enrique Otarola , Daniel Quero

This work investigates an elliptic optimal control problem defined on uncertain domains and discretized by a fictitious domain finite element method and cut elements. Key ingredients of the study are to manage cases considering the usually…

Numerical Analysis · Mathematics 2022-04-06 Aikaterini Aretaki , Efthymios N. Karatzas

We present a new error analysis for finite element methods for a linear-quadratic elliptic optimal control problem with Neumann boundary control and pointwise control constraints. It can be applied to standard finite element methods when…

Numerical Analysis · Mathematics 2024-11-05 Susanne C. Brenner , Li-yeng Sung