@article{nehrani_keyanpour_2016, 
  title={Numerical Solution of Optimal Heating of Temperature Field in Uncertain Environment Modelled by the use of Boundary Control}, 
  abstractNote={In the present paper, optimal heating of temperature field which is modelled as a boundary optimal control problem, is investigated in the uncertain environments and then it is solved numerically. In physical modelling, a partial differential equation with stochastic input and stochastic parameter are applied as the constraint of the optimal control problem. Controls are implemented as Dirichlet boundary conditions and representing the heating elements on the boundary of the field. In numerical quantification, stochas-tic input and parameter are approximated via Karhunen-Loéve expansion and inserted to the problem. In fact, for numerical discretization of the problem stochastic Galerkin method is applied to generalize polynomial chaos. Numerical optimization is performed via gradient method. The problem is fully implemented and in order to show the applicability of the method, numerical examples are solved and numerical results are represented through figures.}, 
  author={Nehrani and Keyanpour}, 
  year={2016}
  }