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.

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 : 10.1051/m2an/2011013
Classification : 65N12, 65N30, 65M12, 93C20
Mots clés : laser surface hardening of steel, semi-linear parabolic equation, optimal control, error estimates, discontinuous Galerkin finite element method
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     title = {An $hp${-Discontinuous} {Galerkin} {Method} for the {Optimal} {Control} {Problem} of {Laser} {Surface} {Hardening} of {Steel}},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
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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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