Related papers: Space-time finite element methods for distributed …
We consider space-time tracking optimal control problems for linear para\-bo\-lic initial boundary value problems that are given in the space-time cylinder $Q = \Omega \times (0,T)$, and that are controlled by the right-hand side…
We consider a distributed optimal control problem subject to a parabolic evolution equation as constraint. The control will be considered in the energy norm of the anisotropic Sobolev space $[H_{0;,0}^{1,1/2}(Q)]^\ast$, such that the state…
We consider the null controllability problem for the wave equation, and analyse a stabilized finite element method formulated on a global, unstructured spacetime mesh. We prove error estimates for the approximate control given by the…
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 analyze the finite element discretization of distributed elliptic optimal control problems with variable energy regularization, where the usual $L^2(\Omega)$ norm regularization term with a constant regularization parameter $\varrho$ is…
We analyze space-time finite element methods for the numerical solution of distributed parabolic optimal control problems with energy regularization in the Bochner space $L^2(0,T;H^{-1}(\Omega))$. By duality, the related norm can be…
We propose, analyze, and test new robust iterative solvers for systems of linear algebraic equations arising from the space-time finite element discretization of reduced optimality systems defining the approximate solution of hyperbolic…
In this paper, we consider a class of time-optimal control problems governed by linear parabolic equations with mixed control-state constraints and end-point constraints, and without Tikhonov regularization term in the objective function.…
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…
We consider a space-time finite element method for the numerical solution of a distributed tracking-type optimal control problem subject to the heat equation with state constraints. The cost or regularization term is formulated in an…
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 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…
This work is concerned with the optimal control problems governed by a 1D wave equation with variable coefficients and the control spaces $\mathcal M_T$ of either measure-valued functions $L_{w^*}^2(I,\mathcal M(\Omega))$ or vector measures…
This work is devoted to the reconstruction of the initial temperature in the backward heat equation using the space-time finite element method on fully unstructured space-time simplicial meshes proposed by Steinbach (2015). Such a severely…
In this paper, we investigate an optimal control problem governed by parabolic equations with measure-valued controls over time. We establish the well-posedness of the optimal control problem and derive the first-order optimality condition…
We consider standard tracking-type, distributed elliptic optimal control problems with $L^2$ regularization, and their finite element discretization. We are investigating the $L^2$ error between the finite element approximation $u_{\varrho…
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…
In this paper we propose a new finite element method for solving elliptic optimal control problems with pointwise state constraints, including the distributed controls and the Dirichlet or Neumann boundary controls. The main idea is to use…
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 paper we discuss the numerical solution of elliptic distributed optimal control problems with state or control constraints when the control is considered in the energy norm. As in the unconstrained case we can relate the…