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
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by Sudipto Chowdhury, Thirupathi Gudi and A. K. Nandakumaran PDF

Math. Comp. 86 (2017), 1103-1126 Request permission

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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