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

Chowdhury, Sudipto; Gudi, Thirupathi; Nandakumaran, A.

doi:10.1090/mcom/3125

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
MathSciNet review: 3614013
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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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