A dual weighted residual method for an optimal control problem of laser surface hardening of steel

The main focus of this article is on analyzing and implementing a dual weighted residual (DWR) approach for an optimal control problem of laser surface hardening of steel. The problem which is governed by a dynamical system consisting of a semi-linear parabolic equation and an ordinary differential equation is discretized using the finite element method. A posteriori error estimates are derived and an adaptive algorithm is formulated. The numerical experiments justify the theoretical results obtained.