Related papers: Finite element error analysis for measure-valued o…
In this paper, we consider an infinite horizon Linear-Quadratic-Gaussian control problem with controlled and costly measurements. A control strategy and a measurement strategy are co-designed to optimize the trade-off among control…
This work is motivated by the need to study the impact of data uncertainties and material imperfections on the solution to optimal control problems constrained by partial differential equations. We consider a pathwise optimal control…
We consider linear model reduction in both the control and state variables for unconstrained linear-quadratic optimal control problems subject to time-varying parabolic PDEs. The first-order optimality condition for a state-space reduced…
This work is concerned with a class of optimal control problems governed by a partial differential equation that are motivated by an application in radiotherapy treatment planning, where the primary design objective is to minimize the…
Controlling the shapes of surfaces provides a novel way to direct self-assembly of colloidal particles on those surfaces and may be useful for material design. This motivates the investigation of an optimal control problem for surface shape…
We consider the discretization of parabolic initial boundary value problems by finite element methods in space and a Runge-Kutta time stepping scheme. Order optimal a-priori error estimates are derived in an energy-norm under natural…
We consider an elliptic optimal control problem where the objective functional contains an integral along a surface of codimension 1, also known as a hypersurface. In particular, we use a fidelity term that encourages the state to take…
We consider an unregularized optimal control problem subject to the steady-state Navier-Stokes equations. We derive the existence of optimal solutions and prove first- and second-order optimality conditions. To approximate solutions to the…
We study an optimal control problem on infinite time horizon with semimartingale strategies, random coefficients and regime switching. The value function and the optimal strategy can be characterized in terms of three systems of backward…
This paper is concerned with fully discrete finite element methods for approximating variational solutions of nonlinear stochastic elastic wave equations with multiplicative noise. A detailed analysis of the properties of the weak solution…
In this paper we consider the initial-boundary value problem for the time-dependent Maxwell-Schr\"{o}dinger equations, which arises in the interaction between the matter and the electromagnetic field for the semiconductor quantum devices. A…
Optimal control problems for semilinear elliptic equations with control costs in the space of bounded variations are analysed. BV-based optimal controls favor piecewise constant, and hence 'simple' controls, with few jumps. Existence of…
In ergodic singular stochastic control problems, a decision-maker can instantaneously adjust the evolution of a state variable using a control of bounded variation, with the goal of minimizing a long-term average cost functional. The cost…
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…
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…
Method-of-lines discretizations are demanding test problems for stiff integration methods. However, for PDE problems with known analytic solution the presence of space discretization errors or the need to use codes to compute reference…
Variational time discretization schemes are getting of increasing importance for the accurate numerical approximation of transient phenomena. The applicability and value of mixed finite element methods (MFEM) in space for simulating…
The article examines a linear-quadratic Neumann control problem that is governed by a non-coercive elliptic equation. Due to the non-self-adjoint nature of the linear control-to-state operator, it is necessary to independently study both…
This article examines the Dirichlet boundary control problem governed by the Poisson equation, where the control variables are square integrable functions defined on the boundary of a two dimensional bounded, convex, polygonal domain. It…
This work is concerned with quasi-optimal a-priori finite element error estimates for the obstacle problem in the $L^2$-norm. The discrete approximations are introduced as solutions to a finite element discretization of an accordingly…