Numerical method of one optimal control problem solution for semilinear elliptic equation with discontinuous coefficients and solution

Non-linear optimal control problem for semilinear elliptic equation with discontinuous coefficients and solution, with controls involved in the coefficients is considered and investigated in the work. Method of difference approximation of extremum problem is stated. The convergence rate of the approximations with respect to the state and the functional is estimated, weak convergence with respect to the control is established. The approximations are regularized by Tikhonov.