Related papers: Solution of the Optimal Control Problem for the Ca…
We study the numerical solution of a Cahn-Hilliard/Allen-Cahn system with strong coupling through state and gradient dependent non-diagonal mobility matrices. A fully discrete approximation scheme in space and time is proposed which…
This paper analyzes an interface-unfitted numerical method for distributed optimal control problems governed by elliptic interface equations. We follow the variational discretization concept to discretize the optimal control problems, and…
This paper is concerned with a boundary control problem for the Cahn--Hilliard equation coupled with dynamic boundary conditions. In order to handle the control problem, we restrict our analysis to the case of regular potentials defined on…
We consider control-constrained linear-quadratic optimal control problems on evolving surfaces. In order to formulate well-posed problems, we prove existence and uniqueness of weak solutions for the state equation, in the sense of…
In this work, we investigate optimal control of a Brinkman equation couple with sixth-order Cahn-Hilliard equation. The Cahn-Hilliard equation is endowed with a source term accounting for mass exchange and the velocity equation contains a…
In the paper, we propose solving optimization problems (OPs) and understanding the Newton method from the optimal control view. We propose a new optimization algorithm based on the optimal control problem (OCP). The algorithm features…
We present a combination technique based on mixed differences of both spatial approximations and quadrature formulae for the stochastic variables to solve efficiently a class of Optimal Control Problems (OCPs) constrained by random partial…
We study an optimal distributed control problem associated to a stochastic Cahn-Hilliard equation with a classical double-well potential and Wiener multiplicative noise, where the control is represented by a source-term in the definition of…
This paper proposes an algorithmic technique for a class of optimal control problems where it is easy to compute a pointwise minimizer of the Hamiltonian associated with every applied control. The algorithm operates in the space of relaxed…
In this paper, we investigate a distributed optimal control problem for a convective viscous Cahn-Hilliard system with dynamic boundary conditions. Such systems govern phase separation processes between two phases taking place in an…
An optimal control problem driven by an ordinary differential equation under continuous state constraints is considered in this study. From an operational point of view, we introduce a discrete state constraints optimal control problem and…
In this paper we study a distributed optimal control problem for a nonlocal convective Cahn--Hilliard equation with degenerate mobility and singular potential in three dimensions of space. While the cost functional is of standard tracking…
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…
We investigate a distributed optimal control problem for a phase field model of Cahn-Hilliard type. The model describes two-species phase segregation on an atomic lattice under the presence of diffusion; it has been recently introduced by…
Optimal Control Problems consist on the optimisation of an objective functional subjected to a set of Ordinary Differential Equations. In this work, we consider the effects on the stability of the numerical solution when this optimisation…
The article discusses the gradient discretisation method (GDM) for distributed optimal control problems governed by diffusion equation with pure Neumann boundary condition. Using the GDM framework enables to develop an analysis that…
The optimal control of a mechanical system is of crucial importance in many realms. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion…
The Cahn-Hilliard system has been used to describe a wide number of phase separation processes, from co-polymer systems to lipid membranes. In this work the convergence properties of a closest-point based scheme is investigated. In place of…
We consider a one dimensional elliptic distributed optimal control problem with pointwise constraints on the derivative of the state. By exploiting the variational inequality satisfied by the derivative of the optimal state, we obtain…
In this article we present a refined convergence analysis for a second order accurate in time, fourth order finite difference numerical scheme for the 3-D Cahn-Hilliard equation, with an improved convergence constant. A modified backward…