Related papers: Non-Conforming Finite Element Method For Constrain…
We consider an optimization problem related to elliptic PDEs of the form $-{\rm div}(a(x)\nabla u)=f$ with Dirichlet boundary condition on a given domain $\Omega$. The coefficient $a(x)$ has to be determined, in a suitable given class of…
We study solution techniques for a linear-quadratic optimal control problem involving fractional powers of elliptic operators. These fractional operators can be realized as the Dirichlet-to-Neumann map for a nonuniformly elliptic problem…
A discretization of an optimal control problem of a stochastic parabolic equation driven by multiplicative noise is analyzed. The state equation is discretized by the continuous piecewise linear element method in space and by the backward…
The paper considers the optimal control problem of inventory of a discrete product in regeneration scheme with a Poisson flow of customer requirements. In the system deferred demand is allowed, the volume of which is limited by a given…
We construct and analyze a multiscale finite element method for an elliptic distributed optimal control problem with pointwise control constraints, where the state equation has rough coefficients. We show that the performance of the…
The optimal control of problems that are constrained by partial differential equations with uncertainties and with uncertain controls is addressed. The Lagrangian that defines the problem is postulated in terms of stochastic functions, with…
In this paper we study the conditioning of optimal control problems constrained by linear parabolic equations with Neumann boundary conditions. While we concentrate on a given end-time target function the results hold also when the target…
It is proved in Chon{\'e} and Le Meur (2001) that the problem of minimizing a Dirichlet-like functional of the function $u\_h$ discretized with $P\_1$ Finite Elements, under the constraint that $u\_h$ be convex, cannot converge. Here, we…
We prove the convergence of the fixed-point (also called thresholding) algorithm in three optimal control problems under large volume constraints. This algorithm was introduced by C\'ea, Gioan and Michel, and is of constant use in the…
In this paper, we study the biharmonic equation with the Navier boundary conditions in a polygonal domain. In particular, we propose a method that effectively decouples the 4th-order problem into a system of Poisson equations. Different…
We study a finite-element based space-time discretisation for the 2D stochastic Navier-Stokes equations in a bounded domain supplemented with no-slip boundary conditions. We prove optimal convergence rates in the energy norm with respect to…
In this article, the limiting behavior of the solution $\bar u_s$ of the optimal control problem subjected to the fractional Poisson equation $$(-\Delta)^s u_s(x)=f_s(x), \quad x\in \Omega$$ defined on domain $\Omega$ bounded by smooth…
The paper deals with a stochastic Galerkin approximation of elliptic Dirichlet boundary control problems with random input data. The expectation of a tracking cost functional with the deterministic constrained control is minimized. Error…
In this paper we study the exact boundary controllability for the following Boussinesq equation with variable physical parameters: \begin{array}{lll} \rho(x)y_{tt}=-(\sigma(x)y_{xx})_{xx}+(q(x)y_x)_x-(y^2)_{xx},&&t>0,~x\in(0,l),\\…
In this paper we prove necessary conditions for optimality of a stochastic control problem for a class of stochastic partial differential equations that is controlled through the boundary. This kind of problems can be interpreted as a…
We introduce a family of hybrid discretisations for the numerical approximation of optimal control problems governed by the equations of immiscible displacement in porous media. The proposed schemes are based on mixed and discontinuous…
We consider the study of a numerical scheme for an initial- and Dirichlet boundary- value problem for a nonlinear Schr\"odinger equation. We approximate the solution using a, local (non-uniform) two level scheme in time (see C. Besse [6]…
Optimal control problems without control costs in general do not possess solutions due to the lack of coercivity. However, unilateral constraints together with the assumption of existence of strictly positive solutions of a pre-adjoint…
We consider the 1D nonlinear Schr\"odinger equation with bilinear control. In the case of Neumann boundary conditions, local exact controllability of this equation near the ground state has been proved by Beauchard and Laurent in…
We present a regularization strategy that leads to well-conditioned boundary integral equation formulations of Helmholtz equations with impedance boundary conditions in two-dimensional Lipschitz domains. We consider both the case of…