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An hp-Discontinuous Galerkin Method for the Optimal Control Problem of Laser Surface Hardening of Steel

Published online by Cambridge University Press:  28 June 2011

Gupta Nupur  and
Nataraj Neela
Gupta Nupur
Affiliation:
Department of Mathematics, Indian Institute of Technology Bombay, Powai, 400076 Mumbai, India. nupur@math.iitb.ac.in; neela@math.iitb.ac.in
Nataraj Neela
Affiliation:
Department of Mathematics, Indian Institute of Technology Bombay, Powai, 400076 Mumbai, India. nupur@math.iitb.ac.in; neela@math.iitb.ac.in
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Abstract

In this paper, we discuss an hp-discontinuous Galerkin finite element method (hp-DGFEM) for the laser surface hardening of steel, which is a constrained optimal control problem governed by a system of differential equations, consisting of an ordinary differential equation for austenite formation and a semi-linear parabolic differential equation for temperature evolution. The space discretization of the state variable is done using an hp-DGFEM, time and control discretizations are based on a discontinuous Galerkin method. A priori error estimates are developed at different discretization levels. Numerical experiments presented justify the theoretical order of convergence obtained.

Keywords

Laser surface hardening of steelsemi-linear parabolic equationoptimal controlerror estimatesdiscontinuous Galerkin finite element method
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 45 , Issue 6 , November 2011 , pp. 1081 - 1113
Copyright
© EDP Sciences, SMAI, 2011

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