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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 a priori error estimates are derived for full discretization (in space and time) of time-optimal control problems. Various convergence results for the optimal time and the control variable are proved under different…

Optimization and Control · Mathematics 2018-09-19 Lucas Bonifacius , Konstantin Pieper , Boris Vexler

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

This work presents and analyzes space-time finite element methods on fully unstructured simplicial space-time meshes for the numerical solution of parabolic optimal control problems. Using Babu\v{s}ka's theorem, we show well-posedness of…

Numerical Analysis · Mathematics 2020-04-07 Ulrich Langer , Olaf Steinbach , Fredi Tröltzsch , Huidong Yang

This paper analyzes an interface-unfitted numerical method for distributed optimal control problems governed by elliptic interface equations. We follow the variational discretization concept to discretize the optimal control problems, and…

Numerical Analysis · Mathematics 2018-10-05 Tao Wang , Chaochao Yang , 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

This work develops and analyzes a variational-monolithic unfitted finite element formulation of a linear fluid-structure interaction problem in Eulerian coordinates with a fixed interface. The overall discretization is based on a backward…

Numerical Analysis · Mathematics 2026-03-27 Stefan Frei , Tobias Knoke , Marc C. Steinbach , Anne-Kathrin Wenske , Thomas Wick

We consider control-constrained linear-quadratic optimal control problems on evolving surfaces. In order to formulate well-posed problems, we prove existence and uniqueness of weak solutions for the state equation, in the sense of…

Optimization and Control · Mathematics 2015-03-19 Morten Vierling

We consider a space-time finite element method on fully unstructured simplicial meshes for optimal sparse control of semilinear parabolic equations. The objective is a combination of a standard quadratic tracking-type functional including a…

Numerical Analysis · Mathematics 2020-04-01 Ulrich Langer , Olaf Steinbach , Fredi Tröltzsch , Huidong Yang

Many problems in electrical engineering or fluid mechanics can be modeled by parabolic-elliptic interface problems, where the domain for the exterior elliptic problem might be unbounded. A possibility to solve this class of problems…

Numerical Analysis · Mathematics 2018-05-15 Christoph Erath , Robert Schorr

This paper studies an optimal control problem governed by a semilinear elliptic equation, in which the control acts in a multiplicative or bilinear way as the reaction coefficient of the equation. We focus on the numerical discretization of…

Optimization and Control · Mathematics 2025-06-25 Eduardo Casas , Konstantinos Chrysafinos , Mariano Mateos

We consider the integral definition of the fractional Laplacian and analyze a linear-quadratic optimal control problem for the so-called fractional heat equation; control constraints are also considered. We derive existence and uniqueness…

Optimization and Control · Mathematics 2020-06-24 Christian Glusa , Enrique Otarola

In this paper, the optimal strong error estimates for stochastic parabolic optimal control problem with additive noise and integral state constraint are derived based on time-implicit and finite element discretization. The continuous and…

Optimization and Control · Mathematics 2025-05-13 Qiming Wang , Wanfang Shen , Wenbin Liu

In the context of unfitted finite element discretizations the realization of high order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. We consider a new unfitted finite element method…

Numerical Analysis · Mathematics 2017-06-27 Christoph Lehrenfeld , Arnold Reusken

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

A discretization of an optimal control problem of a stochastic parabolic equation driven by multiplicative noise is analyzed. The state equation is discretized by the continuous piecewise linear element method in space and by the backward…

Numerical Analysis · Mathematics 2021-02-23 Binjie Li

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

Immersed finite element (IFE) methods are a group of long-existing numerical methods for solving interface problems on unfitted meshes. A core argument of the methods is to avoid mesh regeneration procedure when solving moving interface…

Numerical Analysis · Mathematics 2020-05-01 Ruchi Guo

We design and analyze solution techniques for a linear-quadratic optimal control problem involving the integral fractional Laplacian. We derive existence and uniqueness results, first order optimality conditions, and regularity estimates…

Optimization and Control · Mathematics 2020-10-09 Marta D'Elia , Christian Glusa , Enrique Otarola

The aim of this paper is to extend the global error estimation and control addressed in Lang and Verwer [SIAM J. Sci. Comput. 29, 2007] for initial value problems to finite difference solutions of semilinear parabolic partial differential…

Numerical Analysis · Mathematics 2018-02-16 Kristian Debrabant , Jens Lang