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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 L₂ -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.
Chowdhury et al. (Fri,) studied this question.