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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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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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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