Different approaches for Dirichlet and Neumann boundary optimal control

Giorgio Bornia, Saikanth Ratnavale

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

In this paper we consider different methods for formulating boundary optimal control problems of either Dirichlet or Neumann type. On one hand, standard approaches typically have the drawback of searching for the optimal controls in proper sub-spaces of natural trace spaces. Therefore, we consider alternative formulations with lifting functions that have several advantages. First of all, boundary controls can be determined on natural trace spaces, without additional regularity as required by standard approaches. This also leads to numerical discretizations that have the same rate of convergence for the unknowns defined on the domain and for those on the boundary. A potential drawback of the method consists in the use of control functions defined over the problem domain instead of on its boundary, thus increasing the number of degrees of freedom of the problem. This drawback can be compensated by using lifting functions with restricted support, whose boundary contains the control boundary under interest. Numerical results solving the optimality systems in an all-at-once approach show that it is possible to use restricted functions which do not substantially change the minimum value of the target functional with respect to the case of lifting functions with non-restricted support.

Original languageEnglish
Title of host publicationInternational Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2017
EditorsCharalambos Tsitouras, Theodore Simos, Theodore Simos, Theodore Simos, Theodore Simos, Theodore Simos
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735416901
DOIs
StatePublished - Jul 10 2018
EventInternational Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2017 - Thessaloniki, Greece
Duration: Sep 25 2017Sep 30 2017

Publication series

NameAIP Conference Proceedings
Volume1978
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

ConferenceInternational Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2017
Country/TerritoryGreece
CityThessaloniki
Period09/25/1709/30/17

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