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.
@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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {45},
year = {2011},
pages = {1081-1113},
doi = {10.1051/m2an/2011013},
zbl = {1269.65064},
language = {en},
url = {http://dml.mathdoc.fr/item/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 - Modélisation Mathématique et Analyse Numérique, Tome 45 (2011) pp. 1081-1113. doi : 10.1051/m2an/2011013. http://gdmltest.u-ga.fr/item/M2AN_2011__45_6_1081_0/
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