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

• Volume: 45, Issue: 6, page 1081-1113
• ISSN: 0764-583X

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## Abstract

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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.

## How to cite

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Nupur, Gupta, and Neela, Nataraj. "An hp-Discontinuous Galerkin Method for the Optimal Control Problem of Laser Surface Hardening of Steel." ESAIM: Mathematical Modelling and Numerical Analysis 45.6 (2011): 1081-1113. <http://eudml.org/doc/276342>.

@article{Nupur2011,
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. },
author = {Nupur, Gupta, Neela, Nataraj},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Laser surface hardening of steel; semi-linear parabolic equation; optimal control; error estimates; discontinuous Galerkin finite element method; laser surface hardening of steel; semi-linear parabolic equation; discontinuous Galerkin finite element method; numerical experiments},
language = {eng},
month = {6},
number = {6},
pages = {1081-1113},
publisher = {EDP Sciences},
title = {An hp-Discontinuous Galerkin Method for the Optimal Control Problem of Laser Surface Hardening of Steel},
url = {http://eudml.org/doc/276342},
volume = {45},
year = {2011},
}

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
DA - 2011/6//
PB - EDP Sciences
VL - 45
IS - 6
SP - 1081
EP - 1113
AB - 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.
LA - eng
KW - Laser surface hardening of steel; semi-linear parabolic equation; optimal control; error estimates; discontinuous Galerkin finite element method; laser surface hardening of steel; semi-linear parabolic equation; discontinuous Galerkin finite element method; numerical experiments
UR - http://eudml.org/doc/276342
ER -

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