Displaying similar documents to “A certified reduced basis method for parametrized elliptic optimal control problems”

A Posteriori Error Estimation for Reduced Order Solutions of Parametrized Parabolic Optimal Control Problems

Mark Kärcher, Martin A. Grepl (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We consider the efficient and reliable solution of linear-quadratic optimal control problems governed by parametrized parabolic partial differential equations. To this end, we employ the reduced basis method as a low-dimensional surrogate model to solve the optimal control problem and develop error estimation procedures that provide rigorous bounds for the error in the optimal control and the associated cost functional. We show that our approach can be applied to problems involving control...

Error Estimates for the Numerical Approximation of Semilinear Elliptic Control Problems with Finitely Many State Constraints

Eduardo Casas (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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The goal of this paper is to derive some error estimates for the numerical discretization of some optimal control problems governed by semilinear elliptic equations with bound constraints on the control and a finitely number of equality and inequality state constraints. We prove some error estimates for the optimal controls in the norm and we also obtain error estimates for the Lagrange multipliers associated to the state constraints as well as for the optimal states...

An error analysis of adaptive finite element methods for distributed elliptic control problems with control constraints

Michael Hintermüller, Ronald H.W. Hoppe, Yuri Iliash, Michael Kieweg (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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We present an error analysis of adaptive finite element approximations of distributed control problems for second order elliptic boundary value problems under bound constraints on the control. The error analysis is based on a residual-type error estimator that consists of edge and element residuals. Since we do not assume any regularity of the data of the problem, the error analysis further invokes data oscillations. We prove reliability and efficiency of the error estimator and provide...