Volume 20, Number 3, July-September 2014
|Page(s)||803 - 822|
|Published online||05 June 2014|
New regularity results and improved error estimates for optimal control problems with state constraints∗
Departmento de Matemática Aplicada y Ciencias de la Computación,
E.T.S.I. Industriales y de Telecomunicación, Universidad de Cantabria,
2 Departmento de Matemáticas, E.P.I. Gijón, Universidad de Oviedo, Campus de Gijón, 33203 Gijón, Spain
3 Center for Mathematical Sciences, Technische Universität München, Bolzmannstrasse 3, 85748 Garching b. München, Germany
Revised: 25 November 2013
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 L2(Ω) of the control variable is h | log h | in dimensions 2 and 3.
Mathematics Subject Classification: 49K20 / 49M05 / 49M25 / 65N30 / 65N15
Key words: Optimal control / state constraints / elliptic equations / Borel measures / error estimates
© EDP Sciences, SMAI 2014
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