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We tackle a nonlinear optimal control problem for a stochastic differential equation in Euclidean space and its state-linear counterpart for the Fokker-Planck-Kolmogorov equation in the space of probabilities. Our approach is founded on a…

Optimization and Control · Mathematics 2024-09-23 Roman Chertovskih , Nikolay Pogodaev , Maxim Staritsyn , A. Pedro Aguiar

The optimal control input for linear systems can be solved from algebraic Riccati equation (ARE), from which it remains questionable to get the form of the exact solution. In engineering, the acceptable numerical solutions of ARE can be…

Systems and Control · Electrical Eng. & Systems 2022-01-07 Shengbo Wang , Shiping Wen , Kaibo Shi , Song Zhu , Tingwen Huang

We propose a fourth-order cut-cell method for solving the two-dimensional advection-diffusion equation with moving boundaries on a Cartesian grid. We employ the ARMS technique to give an explicit and accurate representation of moving…

Numerical Analysis · Mathematics 2025-03-24 Kaiyi Liang , Yuke Zhu , Jiyu Liu , Qinghai Zhang

We solve the convection-diffusion equation using a coupling of cell-centered finite volume (FV) and discontinuous Galerkin (DG) methods. The domain is divided into disjoint regions assigned to FV or DG, and the two methods are coupled…

Numerical Analysis · Mathematics 2025-09-30 Maurice S. Fabien

We analyze a high order unfitted hybridizable discontinuous Galerkin (HDG) method for an optimal control problem governed by a convection-diffusion equation posed in a domain with piecewise-wise $\mathcal{C}^2$ boundary $\partial \Omega$.…

Numerical Analysis · Mathematics 2026-04-02 Esteban Henríquez , Manuel Solano

We propose a fourth-order unfitted characteristic finite element method to solve the advection-diffusion equation on time-varying domains. Based on a characteristic-Galerkin formulation, our method combines the cubic MARS method for…

Numerical Analysis · Mathematics 2022-06-09 Chuwen Ma , Qinghai Zhang , Weiying Zheng

We present a novel energy-based numerical analysis of semilinear diffusion-reaction boundary value problems. Based on a suitable variational setting, the proposed computational scheme can be seen as an energy minimisation approach. More…

Numerical Analysis · Mathematics 2022-02-16 Mario Amrein , Pascal Heid , Thomas P. Wihler

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

This article presents a high order conservative flux optimization (CFO) finite element method for the elliptic diffusion equations. The numerical scheme is based on the classical Galerkin finite element method enhanced by a flux…

Numerical Analysis · Mathematics 2019-11-13 Yujie Liu , Yue Feng , Ran Zhang

This article provides quasi-optimal a priori error estimates for an optimal control problem constrained by an elliptic obstacle problem where the finite element discretization is carried out using the symmetric interior penalty…

Numerical Analysis · Mathematics 2023-12-21 Harbir Antil , Rohit Khandelwal , Umarkhon Rakhimov

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 consider a distributed optimal control problem governed by an elliptic convection diffusion PDE, and propose a hybridizable discontinuous Galerkin (HDG) method to approximate the solution. We use polynomials of degree $k+1$ and $k \ge 0$…

Numerical Analysis · Mathematics 2018-11-27 Weiwei Hu , Jiguang Shen , John R. Singler , Yangwen Zhang , Xiaobo Zheng

We present a new class of high-order accurate numerical algorithms for solving the equations of general-relativistic ideal magnetohydrodynamics in curved spacetimes. In this paper we assume the background spacetime to be given and static,…

Computational Physics · Physics 2018-05-28 Francesco Fambri , Michael Dumbser , Sven Köppel , Luciano Rezzolla , Olindo Zanotti

We introduce reduced order methods as an efficient strategy to solve parametrized non-linear and time dependent optimal flow control problems governed by partial differential equations. Indeed, the optimal control problems require a huge…

Numerical Analysis · Mathematics 2023-08-08 Maria Strazzullo , Zakia Zainib , Francesco Ballarin , Gianluigi Rozza

In this paper, we propose a Galerkin finite element method for the elliptic optimal control problem governed by the Riesz space-fractional PDEs on 2D domains with control variable being discretized by variational discretization technique.…

Numerical Analysis · Mathematics 2022-02-22 Xiaogang Zhu

In this paper, optimal control problems governed by diffusion equations with Dirichlet and Neumann boundary conditions are investigated in the framework of the gradient discretisation method. Gradient schemes are defined for the optimality…

Numerical Analysis · Mathematics 2018-10-09 Jerome Droniou , Neela Nataraj , Devika Shylaja

This work concerns the numerical solution of a coupled system of self-consistent reaction-drift-diffusion-Poisson equations that describes the macroscopic dynamics of charge transport in photoelectrochemical (PEC) solar cells with reactive…

Numerical Analysis · Mathematics 2017-03-16 Michael Harmon , Irene M. Gamba , Kui Ren

We consider an optimal control problem on a bounded domain $\Omega\subset\mathbb{R}^2,$ governed by a parabolic convection--diffusion--reaction equation with pointwise control constraints. We follow the optimize--then--discretize approach,…

Numerical Analysis · Mathematics 2025-12-11 Christos Pervolianakis

We consider the initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space semidiscrete scheme based on the standard Galerkin finite…

Numerical Analysis · Mathematics 2015-06-18 Bangti Jin , Raytcho Lazarov , Yikan Liu , Zhi Zhou

The tempered fractional diffusion equation could be recognized as the generalization of the classic fractional diffusion equation that the truncation effects are included in the bounded domains. This paper focuses on designing the high…

Numerical Analysis · Mathematics 2020-01-03 Leilei Wei , Yinnian He