A priori error estimates for optimal control problems with pointwise constraints on the gradient of the state

Authors:
C. Ortner;W. Wollner
Affiliations:
University of Oxford, Mathematical Institute, 24–29 St. Giles’, OX1 3LB, Oxford, UK;Ruprecht-Karls-Universität Heidelberg, Institut für Angewandte Mathematik, INF 294, 69120, Heidelberg, Germany
Venue:
Numerische Mathematik
Year:
2011

Citing 0
Cited 2

A Priori Error Estimates for Finite Element Discretizations of Parabolic Optimization Problems with Pointwise State Constraints in Time

SIAM Journal on Control and Optimization
A priori error estimates for the finite element discretization of optimal distributed control problems governed by the biharmonic operator

Calcolo: a quarterly on numerical analysis and theory of computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

We analyze a finite element approximation of an elliptic optimal control problem with pointwise bounds on the gradient of the state variable. We derive convergence rates if the control space is discretized implicitly by the state equation. In contrast to prior work we obtain these results directly from classical results for the W 1,∞-error of the finite element projection, without using adjoint information. If the control space is discretized directly, we first prove a regularity result for the optimal control to control the approximation error, based on which we then obtain analogous convergence rates.