In this paper, we discuss an hp-discontinuous Galerkin finiteelement method (hp-DGFEM) for the laser surface hardening ofsteel, which is a constrained optimal control problem governed by asystem of differential equations, consisting of an ordinarydifferential equation for austenite formation and a semi-linearparabolic differential equation for temperature evolution. The spacediscretization of the state variable is done using an hp-DGFEM,time and control discretizations are based on a discontinuousGalerkin method. A priori error estimates are developed atdifferent discretization levels. Numerical experimentspresented justify the theoretical order of convergence obtained.
