相关论文: A~posteriori error analysis for optimization with …
We consider a control-constrained optimal control problem subject to time-harmonic Maxwell's equations; the control variable belongs to a finite-dimensional set and enters the state equation as a coefficient. We derive existence of optimal…
In a previous work, we introduced a discretization scheme for a constrained optimal control problem involving the fractional Laplacian. For such a control problem, we derived optimal a priori error estimates that demand the convexity of the…
A posteriori error estimates are derived in the context of two-dimensional structural elastic shape optimization under the compliance objective. It is known that the optimal shape features are microstructures that can be constructed using…
We propose a new and simpler residual based a posteriori error estimator for finite element approximation of the elliptic obstacle problem. The results in the article are two fold. Firstly, we address the influence of the inhomogeneous…
In this paper we study the a posteriori bounds for a conforming piecewise linear finite element approximation of the Signorini problem. We prove new rigorous a posteriori estimates of residual type in $L^{p}$, for $p \in (4,\infty)$ in two…
In the present work, we derive functional upper bounds for the potential error arising from finite-element boundary-element coupling formulations for a nonlinear Poisson-type transmission problem. The proposed a posteriori error estimates…
We propose an a posteriori error estimator for a sparse optimal control problem: the control variable lies in the space of regular Borel measures. We consider a solution technique that relies on the discretization of the control variable as…
A priori and a posteriori error analysis of $hp$ finite element method for elliptic control problem with Robin boundary condition and boundary observation are presented. are presented. Through the Cl\'ement-type approach and the…
We consider control constrained optimal control problems governed by parameterized stationary Maxwell's system with the Gauss's law. The parameters enter through dielectric, magnetic permeability, and charge density. Moreover, the parameter…
This paper considers the finite element approximation to parabolic optimal control problems with measure data in a nonconvex polygonal domain. Such problems usually possess low regularity in the state variable due to the presence of measure…
We consider the approximation of singularly perturbed linear second-order boundary value problems by $hp$-finite element methods. In particular, we include the case where the associated differential operator may not be coercive. Within this…
In this article, we derive \textit{a posteriori} error estimates for the Dirichlet boundary control problem governed by Stokes equation. An energy-based method has been deployed to solve the Dirichlet boundary control problem. We employ an…
This paper is concerned with the recovery of (approximate) solutions to parabolic problems from incomplete and possibly inconsistent observational data, given on a time-space cylinder that is a strict subset of the computational domain…
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…
Computational approaches to PDE-constrained optimization under uncertainty may involve finite-dimensional approximations of control and state spaces, sample average approximations of measures of risk and reliability, smooth approximations…
We revisit the L2 norm error estimate for the C0 interior penalty analysis of fourth order Dirichlet boundary control problem. The L2 norm estimate for the optimal control is derived under reduced regularity assumption and this analysis can…
In this paper, error estimates are presented for a certain class of optimal control problems with elliptic PDE-constraints. It is assumed that in the cost functional the state is measured in terms of the energy norm generated by the state…
We develop and analyze a posteriori error estimators for a proper orthogonal decomposition-discrete empirical interpolation method (Pod-Deim) reduced order model applied to a parametric Poisson equation posed on a parameter-dependent domain…
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 concerned with the analysis and numerical analysis for the optimal control of first-order magneto-static equations. Necessary and sufficient optimality conditions are established through a rigorous Hilbert space approach.…