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Related papers: A priori Error Estimates for Space-Time Finite Ele…

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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

In this paper we consider a parabolic optimal control problem with a Dirac type control with moving point source in two space dimensions. We discretize the problem with piecewise constant functions in time and continuous piecewise linear…

Numerical Analysis · Mathematics 2018-08-17 Dmitriy Leykekhman , Boris Vexler

In this paper, we employ a space-time finite element method to discretize the parabolic initial-boundary value problem and extend its error analysis with refined estimates on unstructured space-time meshes. We establish higher-order…

Numerical Analysis · Mathematics 2025-03-13 Thi Thanh Mai Ta , Quang Huy Nguyen , Phi Hung Pham

In this paper we investigate a priori error estimates for the space-time Galerkin finite element discretization of an optimal control problem governed by a simplified linear gradient enhanced damage model. The model equations are of a…

Numerical Analysis · Mathematics 2020-04-10 Marita Holtmannspötter , Arnd Rösch , Boris Vexler

In this paper, we consider a class of time-optimal control problems governed by linear parabolic equations with mixed control-state constraints and end-point constraints, and without Tikhonov regularization term in the objective function.…

Optimization and Control · Mathematics 2025-09-04 Huynh Khanh , Bui Trong Kien

In this paper we investigate a priori error estimates for the space-time Galerkin finite element discretization of a simplified semilinear gradient enhanced damage model. The model equations are of a special structure as the state equation…

Optimization and Control · Mathematics 2020-04-14 Marita Holtmannspötter , Arnd Rösch

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

In this paper, we investigate an optimal control problem governed by parabolic equations with measure-valued controls over time. We establish the well-posedness of the optimal control problem and derive the first-order optimality condition…

Optimization and Control · Mathematics 2024-04-04 Wei Gong , Dongdong Liang

We consider a linear-quadratic elliptic optimal control problem with point evaluations of the state variable in the cost functional. The state variable is discretized by conforming linear finite elements. For control discretization, three…

Numerical Analysis · Mathematics 2018-02-09 Niklas Behringer , Dominik Meidner , Boris Vexler

This work discusses the finite element discretization of an optimal control problem for the linear wave equation with time-dependent controls of bounded variation. The main focus lies on the convergence analysis of the discretization…

Optimization and Control · Mathematics 2019-07-26 Sebastian Engel , Philip Trautmann , Boris Vexler

We consider linear model reduction in both the control and state variables for unconstrained linear-quadratic optimal control problems subject to time-varying parabolic PDEs. The first-order optimality condition for a state-space reduced…

Optimization and Control · Mathematics 2025-10-17 Michael Kartmann , Stefan Volkwein

We present a method for the numerical approximation of distributed optimal control problems constrained by parabolic partial differential equations. We complement the first-order optimality condition by a recently developed space-time…

Numerical Analysis · Mathematics 2022-08-23 Thomas Führer , Michael Karkulik

We consider the discretization of parabolic initial boundary value problems by finite element methods in space and a Runge-Kutta time stepping scheme. Order optimal a-priori error estimates are derived in an energy-norm under natural…

Numerical Analysis · Mathematics 2015-07-21 Herbert Egger

We derive error estimates for a linear-quadratic elliptic distributed optimal control problem with pointwise control constraints that can be applied to standard finite element methods and multiscale finite element methods.

Optimization and Control · Mathematics 2024-10-08 Susanne C. Brenner , Li-yeng Sung

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 analyze space-time finite element methods for the numerical solution of distributed parabolic optimal control problems with energy regularization in the Bochner space $L^2(0,T;H^{-1}(\Omega))$. By duality, the related norm can be…

Numerical Analysis · Mathematics 2020-04-22 Ulrich Langer , Olaf Steinbach , Fredi Tröltzsch , Huidong Yang

This article studies a priori error analysis for linear parabolic interface problems with measure data in time in a bounded convex polygonal domain in $\mathbb{R}^2$. We have used the standard continuous fitted finite element discretization…

Numerical Analysis · Mathematics 2021-12-03 Jhuma Sen Gupta

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

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, we consider a state constrained optimal control problem governed by the transient Stokes equations. The state constraint is given by an L2 functional in space, which is required to fulfill a pointwise bound in time. The…

Numerical Analysis · Mathematics 2026-05-20 Dmitriy Leykekhman , Boris Vexler , Jakob Wagner
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