English
Related papers

Related papers: Efficient Solution of State-Constrained Distribute…

200 papers

The ground state energy of a many-electron system can be approximated by an variational approach in which the total energy of the system is minimized with respect to one and two-body reduced density matrices (RDM) instead of many-electron…

Optimization and Control · Mathematics 2017-09-01 Yongfeng Li , Zaiwen Wen , Chao Yang , Yaxiang Yuan

We consider the optimal control of singular nonlinear partial differential equation which is the distributional formulation of the multiphase Stefan type free boundary problem for the general second order parabolic equation. Boundary heat…

Analysis of PDEs · Mathematics 2020-03-03 Ugur G. Abdulla , Evan Cosgrove

In this paper we consider the convergence analysis of adaptive finite element method for elliptic optimal control problems with pointwise control constraints. We use variational discretization concept to discretize the control variable and…

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

Space-time finite element discretizations of time-optimal control problems governed by linear parabolic PDEs and subject to pointwise control constraints are considered. Optimal a priori error estimates are obtained for the control variable…

Optimization and Control · Mathematics 2018-09-14 Lucas Bonifacius , Konstantin Pieper , Boris Vexler

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

We consider an optimal control problem where the state equations are a coupled hyperbolic-elliptic system. This system arises in elastodynamics with piezoelectric effects -- the elastic stress tensor is a function of elastic displacement…

Numerical Analysis · Mathematics 2019-11-05 Harbir Antil , Thomas S. Brown , Francisco-Javier Sayas

We propose a semi-discrete numerical scheme and establish well-posedness of a class of parabolic systems. Such systems naturally arise while studying the optimal control of grain boundary motions. The latter is typically described using a…

Analysis of PDEs · Mathematics 2018-10-26 Harbir Antil , Ken Shirakawa , Noriaki Yamazaki

We consider variational discretization of a parabolic optimal control problem governed by space-time measure controls. For the state discretization we use a Petrov-Galerkin method employing piecewise constant states and piecewise linear and…

Optimization and Control · Mathematics 2019-11-25 Evelyn Herberg , Michael Hinze , Henrik Schumacher

In this paper, we consider the finite element approximation to a parabolic Dirichlet boundary control problem and establish new a priori error estimates. In the temporal semi-discretization we apply the DG(0) method for the state and the…

Numerical Analysis · Mathematics 2023-06-29 Dongdong Liang , Wei Gong , Xiaoping Xie

In this work we present an adaptive Newton-type method to solve nonlinear constrained optimization problems in which the constraint is a system of partial differential equations discretized by the finite element method. The adaptive…

Optimization and Control · Mathematics 2017-06-05 Thomas Carraro , Simon Dörsam , Stefan Frei , Daniel Schwarz

Given an optimal control problem on a heterogeneous body with a periodical structure of particles depending on a small parameter e, we study the asymptotic behavior, as e converges to zero, of the optimal control functional and the optimal…

Analysis of PDEs · Mathematics 2025-10-28 J. I. Díaz , T. A. Shaposhnikova , A. V. Podolskiy

This paper proposes an unconditionally stable numerical method for solving a nonlinear Sobolev model with distributed delay. The proposed computational approach approximates the time derivative by interpolation technique whereas the spatial…

Numerical Analysis · Mathematics 2025-11-04 Eric Ngondiep

We consider locally stabilized, conforming finite element schemes on completely unstructured simplicial space-time meshes for the numerical solution of parabolic initial-boundary value problems with variable, possibly discontinuous in space…

Numerical Analysis · Mathematics 2020-03-23 Ulrich Langer , Andreas Schafelner

We consider the inverse multiphase Stefan problem with homogeneous Dirichlet boundary condition on a bounded Lipschitz domain, where the density of the heat source is unknown in addition to the temperature and the phase transition…

Analysis of PDEs · Mathematics 2020-05-12 Ugur G. Abdulla , Bruno Poggi

This paper proposes an optimal control problem for a parabolic equation with a nonlocal nonlinearity. The system is described by a parabolic equation involving a nonlinear term that depends on the solution and its integral over the domain.…

Optimization and Control · Mathematics 2024-03-20 Cyrille Kenne , Landry Djomegne , Gisèle Mophou

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

We consider a numerical approximation of a linear quadratic control problem constrained by the stochastic heat equation with non-homogeneous Neumann boundary conditions. This involves a combination of distributed and boundary control, as…

Numerical Analysis · Mathematics 2021-09-28 Peter Benner , Tony Stillfjord , Christoph Trautwein

We focus on finding sparse and least-$\ell_1$-norm solutions for unconstrained nonlinear optimal control problems. Such optimization problems are non-convex and non-smooth, nevertheless recent versions of Newton method for under-determined…

Optimization and Control · Mathematics 2019-08-28 Boris Polyak , Andrey Tremba

We propose and analyze a general framework for space-time finite element methods that is based on least-squares finite element methods for solving a first-order reformulation of the thick parabolic obstacle problem. Discretizations based on…

Numerical Analysis · Mathematics 2025-03-12 José Joaquín Carvajal , Davood Damircheli , Thomas Führer , Francisco Fuica , Michael Karkulik

We propose a space-time scheme that combines an unfitted finite element method in space with a discontinuous Galerkin time discretisation for the accurate numerical approximation of parabolic problems with moving domains or interfaces. We…

Numerical Analysis · Mathematics 2023-01-23 Santiago Badia , Hridya Dilip , Francesc Verdugo