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, Volume 45 (2011) no. 6, p. 1081-1113

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.

DOI : https://doi.org/10.1051/m2an/2011013
Classification:  65N12,  65N30,  65M12,  93C20
Keywords: 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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {45},
number = {6},
year = {2011},
pages = {1081-1113},
doi = {10.1051/m2an/2011013},
zbl = {1269.65064},
language = {en},
url = {http://www.numdam.org/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, Volume 45 (2011) no. 6, pp. 1081-1113. doi : 10.1051/m2an/2011013. http://www.numdam.org/item/M2AN_2011__45_6_1081_0/

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