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.
Mots-clés : laser surface hardening of steel, semi-linear parabolic equation, optimal control, error estimates, discontinuous Galerkin finite element method
@article{M2AN_2011__45_6_1081_0,
author = {Nupur, Gupta and Neela, Nataraj},
title = {An $hp${-Discontinuous} {Galerkin} {Method} for the {Optimal} {Control} {Problem} of {Laser} {Surface} {Hardening} of {Steel}},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1081--1113},
publisher = {EDP-Sciences},
volume = {45},
number = {6},
year = {2011},
doi = {10.1051/m2an/2011013},
zbl = {1269.65064},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2011013/}
}
TY - JOUR AU - Nupur, Gupta AU - Neela, Nataraj TI - An $hp$-Discontinuous Galerkin Method for the Optimal Control Problem of Laser Surface Hardening of Steel JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2011 SP - 1081 EP - 1113 VL - 45 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2011013/ DO - 10.1051/m2an/2011013 LA - en ID - M2AN_2011__45_6_1081_0 ER -
%0 Journal Article %A Nupur, Gupta %A Neela, Nataraj %T An $hp$-Discontinuous Galerkin Method for the Optimal Control Problem of Laser Surface Hardening of Steel %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2011 %P 1081-1113 %V 45 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2011013/ %R 10.1051/m2an/2011013 %G en %F M2AN_2011__45_6_1081_0
Nupur, Gupta; Neela, Nataraj. An $hp$-Discontinuous Galerkin Method for the Optimal Control Problem of Laser Surface Hardening of Steel. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 45 (2011) no. 6, pp. 1081-1113. doi : 10.1051/m2an/2011013. http://www.numdam.org/articles/10.1051/m2an/2011013/
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