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.References
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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
- 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
- © Copyright 2016 American Mathematical Society
- Journal: Math. Comp. 86 (2017), 1103-1126
- MSC (2010): Primary 65N30, 65N15, 65N12, 65K10
- DOI: https://doi.org/10.1090/mcom/3125
- MathSciNet review: 3614013