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We consider an abstract framework for the numerical solution of optimal control problems (OCPs) subject to partial differential equations (PDEs). Examples include not only the distributed control of elliptic PDEs such as the Poisson…

Numerical Analysis · Mathematics 2025-05-27 Ulrich Langer , Richard Löscher , Olaf Steinbach , Huidong Yang

We analyze an optimal control problem with pointwise tracking for a fractional semilinear elliptic partial differential equation. The diffusion is characterized by the spectral fractional Laplacian $(-\Delta)^s$ with $s \in (1/2,1)$, a…

Optimization and Control · Mathematics 2026-04-17 Enrique Otarola , Abner J. Salgado

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

In this paper we derive a necessary optimality condition for a local optimal solution of some control problems. These optimal control problems are governed by a semi-linear Vettsel boundary value problem of a linear elliptic equation. The…

Analysis of PDEs · Mathematics 2009-04-08 Yousong Luo

We propose in this paper a multilevel correction method to solve optimal control problems constrained by elliptic equations with the finite element method. In this scheme, solving optimization problem on the finest finite element space is…

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

The article examines a linear-quadratic Neumann control problem that is governed by a non-coercive elliptic equation. Due to the non-self-adjoint nature of the linear control-to-state operator, it is necessary to independently study both…

Optimization and Control · Mathematics 2025-06-25 Thomas Apel , Mariano Mateos , Arnd Rösch

The article discusses the gradient discretisation method (GDM) for distributed optimal control problems governed by diffusion equation with pure Neumann boundary condition. Using the GDM framework enables to develop an analysis that…

Numerical Analysis · Mathematics 2018-10-09 Jerome Droniou , Neela Nataraj , Devika Shylaja

We consider the finite element discretization of an optimal Dirichlet boundary control problem for the Laplacian, where the control is considered in $H^{1/2}(\Gamma)$. To avoid computing the latter norm numerically, we realize it using the…

Numerical Analysis · Mathematics 2018-11-26 Michael Karkulik

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

This paper is concerned with the discretization error analysis of semilinear Neumann boundary control problems in polygonal domains with pointwise inequality constraints on the control. The approximations of the control are piecewise…

Numerical Analysis · Mathematics 2015-05-12 Johannes Pfefferer , Klaus Krumbiegel

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

This article is concerned with the nonconforming finite element method for distributed elliptic optimal control problems with pointwise constraints on the control and gradient of the state variable. We reduce the minimization problem into a…

Numerical Analysis · Mathematics 2021-12-13 Kamana Porwal , Pratibha Shakya

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

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 investigate optimal control problems governed by the elliptic partial differential equation $-\Delta u=f$ subject to Dirichlet boundary conditions on a given domain $\Omega$. The control variable in this setting is the right-hand side…

Optimization and Control · Mathematics 2025-09-03 Giuseppe Buttazzo , Juan Casado-Díaz , Faustino Maestre

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 investigate the numerical approximation of an elliptic optimal control problem which involves a nonconvex local regularization of the $L^q$-quasinorm penalization (with $q\in(0,1)$) in the cost function. Our approach is based on the…

Optimization and Control · Mathematics 2022-09-26 Pedro Merino , Alexander Nenjer

We study an optimal control problem governed by elliptic PDEs with interface, which the control acts on the interface. Due to the jump of the coefficient across the interface and the control acting on the interface, the regularity of…

Numerical Analysis · Mathematics 2023-09-19 Zhiyue Zhang , Kazufumi Ito , Zhilin Li

In this paper we study an optimal control problem (OCP) associated to a linear elliptic equation {on a bounded domain $\Omega$}. The matrix-valued coefficients A of such systems is our control taken in L2 which in particular may comprise…

Optimization and Control · Mathematics 2013-06-12 Thierry Horsin , Peter I. Kogut

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