New regularity results and improved error estimates for optimal control problems with state constraints∗. (25th June 2014)

• Record Type: Journal Article
• Authors: Casas, Eduardo; Mateos, Mariano; Vexler, Boris
• Is Part Of: ESAIM. Volume 20:Number 3(2014:Jul.)
• Page Start: 803
• Page End: 822
• Publication Date: 2014-06-25
• Subjects: System analysis -- Periodicals; Calculus of variations -- Periodicals; Mathematical analysis -- Periodicals; Mathematical optimization -- Periodicals; Control theory -- Periodicals; 515.64
• DOI: 10.1051/cocv/2013084
• Languages: English
• ISSNs: 1292-8119

Abstract

<abstract abstract-type="normal" xml:lang="en"> <title> <x content-type="archive" xml:space="preserve">Abstract</x> </title> <p>In this paper we are concerned with a distributed optimal control problem governed by an elliptic partial differential equation. State constraints of box type are considered. We show that the Lagrange multiplier associated with the state constraints, which is known to be a measure, is indeed more regular under quite general assumptions. We discretize the problem by continuous piecewise linear finite elements and we are able to prove that, for the case of a linear equation, the order of convergence for the error in <italic>L</italic>²(<italic>Ω</italic>) of the control variable is <italic>h</italic> | log <italic>h</italic> | in dimensions 2 and 3.</p> </abstract>