Related papers: A posteriori error estimates for semilinear optima…
We design and analyze solution techniques for a linear-quadratic optimal control problem involving the integral fractional Laplacian. We derive existence and uniqueness results, first order optimality conditions, and regularity estimates…
In this paper we present and analyze a weighted residual a posteriori error estimate for an optimal control problem. The problem involves a nondifferentiable cost functional, a state equation with an integral fractional Laplacian, and…
We adopt the integral definition of the fractional Laplace operator and study an optimal control problem on Lipschitz domains that involves a fractional elliptic partial differential equation (PDE) as state equation and a control variable…
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…
We consider a linear-quadratic elliptic optimal control problem with point evaluations of the state variable in the cost functional. The state variable is discretized by conforming linear finite elements. For control discretization, three…
This work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function. It concerns Symplectic Euler solutions of the Hamiltonian…
We develop a novel a posteriori error estimator for the $L^2$ error committed by the finite element discretization of the solution of the fractional Laplacian. Our a posteriori error estimator takes advantage of the semi-discretization…
We consider finite element solutions to optimization problems, where the state depends on the possibly constrained control through a linear partial differential equation. Basing upon a reduced and rescaled optimality system, we derive a…
We propose and analyze a new discretization technique for a linear-quadratic optimal control problem involving the fractional powers of a symmetric and uniformly elliptic second oder operator; control constraints are considered. Since these…
A general a posteriori error analysis applies to five lowest-order finite element methods for two fourth-order semi-linear problems with trilinear non-linearity and a general source. A quasi-optimal smoother extends the source term to the…
We propose a posteriori error estimators for classical low-order inf-sup stable and stabilized finite element approximations of the Stokes problem with singular sources in two and three dimensional Lipschitz, but not necessarily convex,…
A posteriori error estimates are an important tool to bound discretization errors in terms of computable quantities avoiding regularity conditions that are often difficult to establish. For non-linear and non-differentiable problems,…
This paper is devoted to the a posteriori error analysis of multiharmonic finite element approximations to distributed optimal control problems with time-periodic state equations of parabolic type. We derive a posteriori estimates of…
In this paper, we carry out the numerical analysis of a nonsmooth quasilinear elliptic optimal control problem, where the coefficient in the divergence term of the corresponding state equation is not differentiable with respect to the state…
This paper is concerned with the discretization error analysis of semilinear Neumann boundary control problems in polygonal domains with pointwise inequality constraints on the control. The approximations of the control are piecewise…
In two dimensions, we propose and analyze an a posteriori error estimator for finite element approximations of the stationary Navier Stokes equations with singular sources on Lipschitz, but not necessarily convex, polygonal domains. Under a…
The purpose of this work is to study an optimal control problem for a semilinear elliptic partial differential equation with a linear combination of Dirac measures as a forcing term; the control variable corresponds to the amplitude of such…
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 provide a posteriori error estimates for a discontinuous Galerkin scheme for the parabolic-elliptic Keller-Segel system in 2 or 3 space dimensions. The estimates are conditional, in the sense that an a posteriori computable quantity…
This work reviews goal-oriented a posteriori error control, adaptivity and solver control for finite element approximations to boundary and initial-boundary value problems for stationary and non-stationary partial differential equations,…