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In this article, we formulate a monolithic optimal control method for general time-dependent Fluid-Structure Interaction (FSI) systems with large solid deformation. We consider a displacement-tracking type of objective with a constraint of…

Computational Engineering, Finance, and Science · Computer Science 2022-05-25 Yongxing Wang

The paper introduces a new finite element numerical method for the solution of partial differential equations on evolving domains. The approach uses a completely Eulerian description of the domain motion. The physical domain is embedded in…

Numerical Analysis · Mathematics 2018-08-03 Christoph Lehrenfeld , Maxim A. Olshanskii

This paper addresses the problem of optimally controlling nonlinear systems with norm-bounded disturbances and parametric uncertainties while robustly satisfying constraints. The proposed approach jointly optimizes a nominal nonlinear…

Systems and Control · Electrical Eng. & Systems 2023-09-14 Antoine P. Leeman , Jerome Sieber , Samir Bennani , Melanie N. Zeilinger

A class of parametric optimal control problems governed by semilinear parabolic equations with mixed pointwise constraints is investigated. The perturbations appear in the objective functional, the state equation and in mixed pointwise…

Optimization and Control · Mathematics 2024-02-06 Huynh Khanh

Optimal control of the singular nonlinear parabolic PDE which is a distributional formulation of multidimensional and multiphase Stefan-type free boundary problem is analyzed. Approximating sequence of finite-dimensional optimal control…

Analysis of PDEs · Mathematics 2020-06-16 Ugur G. Abdulla , Evan Cosgrove

The optimal control of two-level systems by time-dependent laser fields is studied using a variational theory. We obtain, for the first time, general analytical expressions for the optimal pulse shapes leading to global maximization or…

Quantum Physics · Physics 2009-11-10 Martin E. Garcia , Ilia Grigorenko

In this work, we present a novel regularized L$_1$ (RL$_1$) finite element spatial discretization scheme for radiation transport problems. We review the recently developed least-squares finite element method in nuclear applications. We then…

Computational Physics · Physics 2016-12-19 Weixiong Zheng , Ryan G. McClarren

This paper develops and analyses numerical approximation for linear-quadratic optimal control problem governed by elliptic interface equations. We adopt variational discretization concept to discretize optimal control problem, and apply an…

Numerical Analysis · Mathematics 2018-06-04 Chao Chao Yang , Tao Wang , Xiaoping Xie

In this work, we study the bilinear optimal stabilization of a non-homogeneous Fokker-Planck equation. We first study the problem of optimal control in a finite-time interval and then focus on the case of the infinite time horizon. We…

Optimization and Control · Mathematics 2022-06-07 K. Ammari , M. Ouzahra , S. Yahyaoui

Computable estimates for the error of finite element discretisations of parabolic problems in the $L^\infty(0,T; L^2)$ norm are developed, which exhibit constant effectivities (the ratio of the estimated error to the true error) with…

Numerical Analysis · Mathematics 2018-03-09 Oliver J. Sutton

This paper is devoted to the controllability of linear systems of two coupled parabolic equations when the coupling involves a space dependent first order term. This system is set on an bounded interval, and the first equation is controlled…

Analysis of PDEs · Mathematics 2017-01-20 Michel Duprez

A finite element method for elliptic problems with discontinuous coefficients is presented. The discontinuity is assumed to take place along a closed smooth curve. The proposed method allows to deal with meshes that are not adapted to the…

Numerical Analysis · Mathematics 2007-07-12 Gunther H. Peichl , Rachid Touzani

A stabilizing/penalty term is often used in finite element methods with discontinuous approximations to enforce connection of discontinuous functions across element boundaries. Removing stabilizers from discontinuous finite element methods…

Numerical Analysis · Mathematics 2019-07-15 Xiu Ye , Shangyou Zhang

Stability of stationary solutions of parabolic equations is conventionally studied by linear stability analysis, Lyapunov functions or lower and upper functions. We discuss here another approach based on differential inequalities written…

Functional Analysis · Mathematics 2012-06-26 A. G. Ramm , V. Volpert

In this paper we propose a nonconforming finite element method for the solution of the ill-posed elliptic Cauchy problem. We prove error estimates using continuous dependence estimates in the $L^2$-norm. The effect of perturbations in data…

Numerical Analysis · Mathematics 2014-06-18 Erik Burman

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 address nonautonomous initial boundary value problems for decoupled linear first-order one-dimensional hyperbolic systems, investigating the phenomenon of finite time stabilization. We establish sufficient and necessary conditions…

Analysis of PDEs · Mathematics 2025-12-10 Irina Kmit , Natalya Lyul'ko

This paper proposes a general formulation for temporal parallelisation of dynamic programming for optimal control problems. We derive the elements and associative operators to be able to use parallel scans to solve these problems with…

Optimization and Control · Mathematics 2022-01-25 Simo Särkkä , Ángel F. García-Fernández

We develop arbitrarily high-order, stationarity-preserving stabilized finite element methods for multidimensional nonlinear hyperbolic balance laws on Cartesian grids. We aim at approximating all the steady states of the problem at hand,…

Numerical Analysis · Mathematics 2026-03-25 Moussa Ziggaf , Davide Torlo , Mario Ricchiuto

In this paper, we study a numerical method for the solution of partial differential equations on evolving surfaces. The numerical method is built on the stabilized trace finite element method (TraceFEM) for the spatial discretization and…

Numerical Analysis · Mathematics 2018-03-23 Christoph Lehrenfeld , Maxim A. Olshanskii , Xianmin Xu