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Error bounds for a Dirichlet boundary control problem based on energy spaces


Authors: Sudipto Chowdhury, Thirupathi Gudi and A. K. Nandakumaran
Journal: Math. Comp. 86 (2017), 1103-1126
MSC (2010): Primary 65N30, 65N15, 65N12, 65K10
DOI: https://doi.org/10.1090/mcom/3125
Published electronically: June 20, 2016
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Abstract: In this article, an alternative energy-space based approach is proposed for the Dirichlet boundary control problem and then a finite-element based numerical method is designed and analyzed for its numerical approximation. A priori error estimates of optimal order in the energy norm and the $ L_2$-norm are derived. Moreover, a reliable and efficient a posteriori error estimator is derived with the help of an auxiliary problem. The theoretical results are illustrated by the numerical experiments.


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Additional Information

Sudipto Chowdhury
Affiliation: Department of Mathematics, Indian Institute of Science, Bangalore - 560012, India
Email: sudipto10@math.iisc.ernet.in

Thirupathi Gudi
Affiliation: Department of Mathematics, Indian Institute of Science, Bangalore - 560012, India
Email: gudi@math.iisc.ernet.in

A. K. Nandakumaran
Affiliation: Department of Mathematics, Indian Institute of Science, Bangalore - 560012, India
Email: nands@math.iisc.ernet.in

DOI: https://doi.org/10.1090/mcom/3125
Keywords: Optimal control, Dirichlet control, finite element, optimal error estimate, adaptive finite element, a posteriori estimates
Received by editor(s): May 19, 2015
Received by editor(s) in revised form: August 27, 2015, and October 7, 2015
Published electronically: June 20, 2016
Article copyright: © Copyright 2016 American Mathematical Society

American Mathematical Society