An hp-Discontinuous Galerkin Method for the Optimal Control Problem of Laser Surface Hardening of Steel
Department of Mathematics, Indian Institute of Technology Bombay, Powai, 400076 Mumbai, India. email@example.com; firstname.lastname@example.org
Revised: 19 March 2011
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.
Mathematics Subject Classification: 65N12 / 65N30 / 65M12 / 93C20
Key words: Laser surface hardening of steel / semi-linear parabolic equation / optimal control / error estimates / discontinuous Galerkin finite element method
© EDP Sciences, SMAI, 2011