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Applied Mathematics & Optimization

, Volume 79, Issue 3, pp 769–795 | Cite as

A Non-overlapping DDM for Optimal Boundary Control Problems Governed by Parabolic Equations

  • Keying Ma
  • Tongjun SunEmail author
Article
  • 43 Downloads

Abstract

In this paper, we consider a non-overlapping domain decomposition method for solving optimal boundary control problems governed by parabolic equations. The whole domain is divided into non-overlapping subdomains, and the global optimal boundary control problem is decomposed into the local problems in these subdomains. The integral mean method is utilized to present an explicit flux calculation on the inter-domain boundary in order to communicate the local problems on the interface between subdomains. We establish the fully parallel and discrete schemes for solving these local problems. A priori error estimates in \(L^2\)-norm are derived for the state, co-state and control variables. Finally, we present numerical experiments to show the validity of the schemes and verify the derived theoretical results.

Keywords

Parabolic equations Optimal boundary control problems Non-overlapping DDM Integral mean method Error estimates 

Mathematics Subject Classification

65N12 65N30 49M25 65K15 

Notes

Acknowledgements

This work is supported by the NSF of China (Nos. 11301300, 11271231).

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.School of MathematicsShandong UniversityJinanChina

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