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Related papers: Error estimates for a bilinear optimal control pro…

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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

Optimal control of bilinear systems has been a well-studied subject in the area of mathematical control. However, techniques for solving emerging optimal control problems involving an ensemble of structurally identical bilinear systems are…

Optimization and Control · Mathematics 2016-01-14 Shuo Wang , Jr-Shin Li

We consider finite element discretizations of Maxwell's equations coupled with a non-local hydrodynamic Drude model that accurately accounts for electron motions in metallic nanostructures. Specifically, we focus on a posteriori error…

Numerical Analysis · Mathematics 2021-08-04 T. Chaumont-Frelet , S. Lanteri , P. Vega

A proof of optimal-order error estimates is given for the full discretization of the Cahn--Hilliard equation with Cahn--Hilliard-type dynamic boundary conditions in a smooth domain. The numerical method combines a linear bulk--surface…

Numerical Analysis · Mathematics 2025-01-15 Nils Bullerjahn , Balázs Kovács

The state-of-the art proof of a global inf-sup condition on mixed finite element schemes does not allow for an analysis of truly indefinite, second-order linear elliptic PDEs. This paper, therefore, first analyses a nonconforming finite…

Numerical Analysis · Mathematics 2014-01-21 Carsten Carstensen , Asha K. Dond , Neela Nataraj , Amiya K. Pani

We derive optimal order a posteriori error estimates for fully discrete approximations of linear Schr\"odinger-type equations, in the $L^\infty(L^2)-$norm. For the discretization in time we use the Crank-Nicolson method, while for the space…

Numerical Analysis · Mathematics 2013-04-10 Theodoros Katsaounis , Irene Kyza

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

We are interested in high-order linear multistep schemes for time discretization of adjoint equations arising within optimal control problems. First we consider optimal control problems for ordinary differential equations and show loss of…

Numerical Analysis · Mathematics 2018-07-24 Giacomo Albi , Michael Herty , Lorenzo Pareschi

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 provide a framework for the numerical approximation of distributed optimal control problems, based on least-squares finite element methods. Our proposed method simultaneously solves the state and adjoint equations and is $\inf$--$\sup$…

Numerical Analysis · Mathematics 2023-08-03 Thomas Führer , Michael Karkulik

We investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time. We consider minimization of an expected value cost over a finite horizon. Hard constraints are introduced first, and then…

Optimization and Control · Mathematics 2011-07-07 Eugenio Cinquemani , Mayank Agarwal , Debasish Chatterjee , John Lygeros

The numerical approximation of convection-dominated problems continues to remain subject of strong interest. Families of stabilization techniques for finite element methods were developed in the past. Adaptive techniques based on a…

Numerical Analysis · Mathematics 2018-03-20 Kristina Schwegler , Marius P. Bruchhäuser , Markus Bause

We propose an {\em implementable} numerical scheme for the discretization of linear-quadratic optimal control problems involving SDEs in higher dimensions with {\em control constraint}. For time discretization, we employ the implicit Euler…

Analysis of PDEs · Mathematics 2024-12-12 Abhishek Chaudhary

The numerical analysis of a family of distributed mixed optimal control problems governed by elliptic variational inequalities (with parameter $\alpha >0$) is obtained through the finite element method when its parameter $h\rightarrow 0$.…

Numerical Analysis · Mathematics 2016-01-05 Mariela C. Olguin , Domingo A. Tarzia

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

This work reviews goal-oriented a posteriori error control, adaptivity and solver control for finite element approximations to boundary and initial-boundary value problems for stationary and non-stationary partial differential equations,…

Numerical Analysis · Mathematics 2024-12-02 Bernhard Endtmayer , Ulrich Langer , Thomas Richter , Andreas Schafelner , Thomas Wick

A general bilinear optimal control problem subject to an infinite-dimensional state equation is considered. Polynomial approximations of the associated value function are derived around the steady state by repeated formal differentiation of…

Optimization and Control · Mathematics 2017-06-19 Tobias Breiten , Karl Kunisch , Laurent Pfeiffer

This work presents the multiharmonic analysis and derivation of functional type a posteriori estimates of a distributed eddy current optimal control problem and its state equation in a time-periodic setting. The existence and uniqueness of…

Optimization and Control · Mathematics 2023-08-10 Monika Wolfmayr

In this paper error analysis for finite element discretizations of Dirichlet boundary control problems is developed. For the first time, optimal discretization error estimates are established in the case of three dimensional polyhedral and…

Numerical Analysis · Mathematics 2024-01-05 Johannes Pfefferer , Boris Vexler

In this chapter, we are concerned with inverse optimal control problems, i.e., optimization models which are used to identify parameters in optimal control problems from given measurements. Here, we focus on linear-quadratic optimal control…

Optimization and Control · Mathematics 2023-11-27 Stephan Dempe , Markus Friedemann , Felix Harder , Patrick Mehlitz , Gerd Wachsmuth