Displaying similar documents to “An optimal order yielding discrepancy principle for simplified regularization of ill-posed problems in Hilbert scales.”

Optimal control and numerical adaptivity for advection–diffusion equations

Luca Dede', Alfio Quarteroni (2005)

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


We propose a general approach for the numerical approximation of optimal control problems governed by a linear advection–diffusion equation, based on a stabilization method applied to the lagrangian functional, rather than stabilizing the state and adjoint equations separately. This approach yields a coherently stabilized control problem. Besides, it allows a straightforward a posteriori error estimate in which estimates of higher order terms are needless. Our a posteriori estimates...

A certified reduced basis method for parametrized elliptic optimal control problems

Mark Kärcher, Martin A. Grepl (2014)

ESAIM: Control, Optimisation and Calculus of Variations


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...