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This paper is concerned with an optimal control problem subject to the $H^1$-critical defocusing semilinear wave equation on a smooth and bounded domain in three spatial dimensions. Due to the criticality of the nonlinearity in the wave…

Optimization and Control · Mathematics 2019-07-08 Karl Kunisch , Hannes Meinlschmidt

We derive a-priori error estimates for the finite-element approximation of a distributed optimal control problem governed by the steady one-dimensional Burgers equation with pointwise box constraints on the control. Here the approximation…

Optimization and Control · Mathematics 2014-11-18 Pedro Martín Merino Rosero

In this paper we discuss the numerical solution of elliptic distributed optimal control problems with state or control constraints when the control is considered in the energy norm. As in the unconstrained case we can relate the…

Numerical Analysis · Mathematics 2023-06-28 Peter Gangl , Richard Löscher , Olaf Steinbach

We investigate the application of a posteriori error estimates to a fractional optimal control problem with pointwise control constraints. Specifically, we address a problem in which the state equation is formulated as an integral form of…

Optimization and Control · Mathematics 2023-10-10 Fangyuan Wang , Qiming Wang , Zhaojie Zhou

An optimal control problem for the linear wave equation with control cost chosen as the BV semi-norm in time is analyzed. This formulation enhances piecewise constant optimal controls and penalizes the number of jumps. Existence of optimal…

Optimization and Control · Mathematics 2018-09-11 Sebastian Engel , Karl Kunisch

The numerical approximation of an optimal control problem with $L^1$-control of a Timoshenko beam is considered and analyzed by using the finite element method. From the practical point of view, inclusion of the $L^1$--norm in the cost…

Optimization and Control · Mathematics 2017-07-25 Erwin Hernández , Pedro Merino

In this paper, we investigate optimal control problems subject to a semilinear elliptic partial differential equations. The cost functional contains a term that measures the size of the support of the control, which is the so-called…

Optimization and Control · Mathematics 2020-02-13 Eduardo Casas , Daniel Wachsmuth

We consider a parabolic optimal control problem with an initial measure control. The cost functional consists of a tracking term corresponding to the observation of the state at final time. Instead of a regularization term in the cost…

Optimization and Control · Mathematics 2020-08-18 Evelyn Herberg , Michael Hinze

We consider an elliptic optimal control problem where the objective functional contains evaluations of the state at a finite number of points. In particular, we use a fidelity term that encourages the state to take certain values at these…

Numerical Analysis · Mathematics 2014-11-19 C. Brett , A. S. Dedner , C. M. Elliott

A finite element analysis of a Dirichlet boundary control problem governed by the linear parabolic equation is presented in this article. The Dirichlet control is considered in a closed and convex subset of the energy space $H^1(\Omega…

Numerical Analysis · Mathematics 2021-11-04 Thirupathi Gudi , Gouranga Mallik , Ramesh Ch. Sau

We study the propagation, observation and control properties of the 1-d wave equation on a bounded interval discretized in space using the quadratic classical finite element approximation. A careful Fourier analysis of the discrete wave…

Analysis of PDEs · Mathematics 2011-12-20 Aurora Marica , Enrique Zuazua

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

We present a fully discrete finite element method for the interior null controllability problem subject to the wave equation. For the numerical scheme, piece-wise affine continuous elements in space and finite differences in time are…

Numerical Analysis · Mathematics 2023-05-10 Erik Burman , Ali Feizmohammadi , Lauri Oksanen

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

This paper is devoted to the a posteriori error analysis of multiharmonic finite element approximations to distributed optimal control problems with time-periodic state equations of parabolic type. We derive a posteriori estimates of…

Optimization and Control · Mathematics 2015-11-19 Ulrich Langer , Sergey Repin , Monika Wolfmayr

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 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

This paper is concerned with a kind of linear-quadratic (LQ) optimal control problem of backward stochastic differential equation (BSDE) with partial information. The cost functional includes cross terms between the state and control, and…

Optimization and Control · Mathematics 2025-09-03 Jialong Li , Zhiyong Yu , Wanying Yue

In this paper, we discuss the numerical approximation of a distributed optimal control problem governed by the von Karman equations, defined in polygonal domains with point-wise control constraints. Conforming finite elements are employed…

Numerical Analysis · Mathematics 2017-09-19 Gouranga Mallik , Neela Nataraj , Jean-Pierre Raymond

We consider the null controllability problem for the wave equation, and analyse a stabilized finite element method formulated on a global, unstructured spacetime mesh. We prove error estimates for the approximate control given by the…

Numerical Analysis · Mathematics 2023-06-13 Erik Burman , Ali Feizmohammadi , Arnaud Munch , Lauri Oksanen