Related papers: Spacetime finite element methods for control probl…
We consider a stabilized finite element method based on a spacetime formulation, where the equations are solved on a global (unstructured) spacetime mesh. A unique continuation problem for the wave equation is considered, where data is…
We present a fully discrete finite element method for the interior null controllability problem subject to the wave equation. For the numerical scheme, piece-wise affine continuous elements in space and finite differences in time are…
We consider space-time tracking type distributed optimal control problems for the wave equation in the space-time domain $Q:= \Omega \times (0,T) \subset {\mathbb{R}}^{n+1}$, where the control is assumed to be in the energy space…
This work presents, analyzes and tests stabilized space-time finite element methods on fully unstructured simplicial space-time meshes for the numerical solution of space-time tracking parabolic optimal control problems with the standard…
In this work, we introduce a new space-time variational formulation of the second-order wave equation, where integration by parts is also applied with respect to the time variable, and a modified Hilbert transformation is used. For this…
This paper deals with the numerical computation of boundary null controls for the 1D wave equation with a potential. The goal is to compute an approximation of controls that drive the solution from a prescribed initial state to zero at a…
This work discusses the finite element discretization of an optimal control problem for the linear wave equation with time-dependent controls of bounded variation. The main focus lies on the convergence analysis of the discretization…
We study the wave equation in an interval with two linearly moving endpoints. We give the exact solution by a series formula, then we show that the energy of the solution decay at the rate $1/t$. We also establish observability results, at…
We consider a stable unique continuation problem for the wave equation where the initial data is lacking and the solution is reconstructed using measurements in some subset of the bulk domain. Typically fairly sophisticated space-time…
We present a finite element (FE) scheme for the numerical approximation of the solution to a non-local Poisson equation involving the one-dimensional fractional Laplacian $(-d_x^2)^s$ on the interval $(-L,L)$. In particular, we include the…
The finite-time control problem of quantum systems is investigated in this paper. We first define finite-time stability and present a finite-time Lyapunov stability criterion for finite-dimensional quantum systems in coherence vector…
A numerical method is proposed for a class of stochastic control problems including singular behavior. This method solves an infinite-dimensional linear program equivalent to the stochastic control problem using a finite element type…
We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…
This thesis aims at investigating the first steps toward an unconditionally stable space-time isogeometric method, based on splines of maximal regularity, for the linear acoustic wave equation. The unconditional stability of space-time…
This paper presents a rigorous finite element framework for solving an optimal control problem governed by the steady Navier-Stokes-Brinkman equations, focusing on identifying a scalar permeability parameter $\gamma$ from local velocity…
We introduce an arbitrary order, stabilized finite element method for solving a unique continuation problem subject to the time-harmonic elastic wave equation with variable coefficients. Based on conditional stability estimates we prove…
By mean of generalized Fourier series and Parseval's equality in weighted $L^{2}$--spaces, we derive a sharp energy estimate for the wave equation in a bounded interval with a moving endpoint. Then, we show the observability, in a sharp…
This work presents and analyzes space-time finite element methods on fully unstructured simplicial space-time meshes for the numerical solution of parabolic optimal control problems. Using Babu\v{s}ka's theorem, we show well-posedness of…
In this work we consider the computational approximation of a unique continuation problem for the Helmholtz equation using a stabilized finite element method. First conditional stability estimates are derived for which, under a convexity…
We consider a space-time finite element method on fully unstructured simplicial meshes for optimal sparse control of semilinear parabolic equations. The objective is a combination of a standard quadratic tracking-type functional including a…