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A posteriori error estimates for an optimal control problem of laser surface hardening of steel

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Abstract

The main focus of this article is on the development of a posteriori error estimates for an optimal control problem of laser surface hardening of steel, governed by a dynamical system consisting of a semi-linear parabolic equation and an ordinary differential equation. A posteriori error estimators are developed for the variables representing temperature, formation of austenite, and laser energy using residual method when a continuous piecewise linear discretization has been used for the finite element approximation of space variables and a discontinuous Galerkin method has been used for time and control discretizations. The error indicators are used in the implementation and numerical results are obtained.

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Authors and Affiliations

  1. ACMAC, Department of Mathematics, University of Crete, Iraklion, 71003, Greece

    Nupur Gupta

  2. Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India

    Neela Nataraj

Authors
  1. Nupur Gupta
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  2. Neela Nataraj
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Correspondence to Neela Nataraj.

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Communicated by Aihui Zhou.

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Gupta, N., Nataraj, N. A posteriori error estimates for an optimal control problem of laser surface hardening of steel. Adv Comput Math 39, 69–99 (2013). https://doi.org/10.1007/s10444-011-9270-8

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  • DOI: https://doi.org/10.1007/s10444-011-9270-8

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