An -Discontinuous Galerkin Method for the Optimal Control Problem of Laser Surface Hardening of Steel
In this paper, we discuss an -discontinuous Galerkin finite element method (-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 -DGFEM, time and control discretizations are based on a discontinuous Galerkin...