| Issue |
ESAIM: M2AN
Volume 45, Number 6, November-December 2011
|
|
|---|---|---|
| Page(s) | 1081 - 1113 | |
| DOI | https://doi.org/10.1051/m2an/2011013 | |
| Published online | 28 June 2011 | |
An hp-Discontinuous Galerkin Method for the Optimal Control Problem of Laser Surface Hardening of Steel
Department of Mathematics, Indian Institute of Technology Bombay, Powai, 400076 Mumbai, India. nupur@math.iitb.ac.in; neela@math.iitb.ac.in
Received:
25
January
2010
Revised:
19
March
2011
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.
Mathematics Subject Classification: 65N12 / 65N30 / 65M12 / 93C20
Key words: Laser surface hardening of steel / semi-linear parabolic equation / optimal control / error estimates / discontinuous Galerkin finite element method
© EDP Sciences, SMAI, 2011
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