Displaying similar documents to “Error Estimates for the Numerical Approximation of Semilinear Elliptic Control Problems with Finitely Many State Constraints”

Error estimates for the finite element discretization of semi-infinite elliptic optimal control problems

Pedro Merino, Ira Neitzel, Fredi Tröltzsch (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper we derive a priori error estimates for linear-quadratic elliptic optimal control problems with finite dimensional control space and state constraints in the whole domain, which can be written as semi-infinite optimization problems. Numerical experiments are conducted to ilustrate our theory.

Error estimates for finite element approximations of elliptic control problems

Walter Alt, Nils Bräutigam, Arnd Rösch (2007)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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We investigate finite element approximations of one-dimensional elliptic control problems. For semidiscretizations and full discretizations with piecewise constant controls we derive error estimates in the maximum norm.

A certified reduced basis method for parametrized elliptic optimal control problems

Mark Kärcher, Martin A. Grepl (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper, we employ the reduced basis method as a surrogate model for the solution of linear-quadratic optimal control problems governed by parametrized elliptic partial differential equations. We present error estimation and dual procedures that provide rigorous bounds for the error in several quantities of interest: the optimal control, the cost functional, and general linear output functionals of the control, state, and adjoint variables. We show that, based on the assumption...