Related papers: A posteriori error analysis for a distributed opti…
We derive optimal order a posteriori error estimates for fully discrete approximations of the initial-boundary value problem for the heat equation. For the discretization in time we apply the fractional-step $\vartheta$-scheme and for the…
We consider some boundary value tracking optimal control problem constrained by a Neumann boundary value problem for some elliptic partial differential equation where the control acts as right-hand side. This optimal control problem can be…
We consider a parabolic optimal control problem with an initial measure control. The cost functional consists of a tracking term corresponding to the observation of the state at final time. Instead of a regularization term in the cost…
In this work, new theoretical results on functional type a posteriori estimates for elliptic optimal control problems with control constraints are presented. More precisely, we derive new, sharp, guaranteed and fully computable lower bounds…
In this article we study a finite horizon optimal control problem with monotone controls. We consider the associated Hamilton-Jacobi-Bellman (HJB) equation which characterizes the value function. We consider the totally discretized problem…
We combine a systematic approach for deriving general a posteriori error estimates for convex minimization problems based on convex duality relations with a recently derived generalized Marini formula. The a posteriori error estimates are…
The efficient and reliable approximation of convection-dominated problems continues to remain a challenging task. To overcome the difficulties associated with the discretization of convection-dominated equations, stabilization techniques…
In this paper, we solve an open problem and obtain a general maximum principle for a stochastic optimal control problem where the control domain is an arbitrary non-empty set and all the coefficients (especially the diffusion term and the…
In this paper, we are concerned with a nonlinear optimal control problem of ordinary differential equations. We consider a discretization of the problem with the discontinuous Galerkin method with arbitrary order $r \in \mathbb{N}\cup…
We consider Poisson's equation with a finite number of weighted Dirac masses as a source term, together with its discretization by means of conforming finite elements. For the error in fractional Sobolev spaces, we propose residual-type a…
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…
We shall develop a fully discrete space-time adaptive method for linear parabolic problems based on new reliable and efficient a posteriori analysis for higher order dG(s) finite element discretisations. The adaptive strategy is motivated…
We study the numerical approximation of linear-quadratic optimal control problems subject to the fractional Laplace equation with its spectral definition. We compute an approximation of the state equation using a discretization of the…
For the pure biharmonic equation and a biharmonic singular perturbation problem, a residual-based error estimator is introduced which applies to many existing nonconforming finite elements. The error estimator involves the local…
We present a method to solve fractional optimal control problems, where the dynamic depends on integer and Caputo fractional derivatives. Our approach consists to approximate the initial fractional order problem with a new one that involves…
We consider the optimal control of a PDE with random source term subject to probabilistic or almost sure state constraints. In the main theoretical result, we provide an exact formula for the Clarke subdifferential of the probability…
In this paper we study the mixed virtual element approximation to an elliptic optimal control problem with boundary observations. The objective functional of this type of optimal control problem contains the outward normal derivatives of…
This paper presents an algorithm to solve non-convex optimal control problems, where non-convexity can arise from nonlinear dynamics, and non-convex state and control constraints. This paper assumes that the state and control constraints…
We consider finite element solutions to quadratic optimization problems, where the state depends on the control via a well-posed linear partial differential equation. Exploiting the structure of a suitably reduced optimality system, we…
Residual-based a~posteriori error estimators are derived for the modified Morley FEM, proposed by Wang, Xu, Hu [J. Comput. Math, 24(2), 2006], for the singularly perturbed biharmonic equation and the nonlinear von K\'arm\'an equations. The…