Using explicit schemes for control problems in continuous casting process

In this article, we solve an optimal control problem of the cooling process in the steel continuous casting, which mathematical formulation is a coeffcient identification problem for Stefan problem with prescribed convection. To minimize a cost function we use a gradient method, state and adjoint state problem being approximated by explicit mesh schemes with variable time steps. Presented numerical results show an advantage in calculations time of this approach in comparison with using implicit mesh schemes.