Estimation of the convection coefficient in elliptic equations

The parameter estimation problem for the convection coefficient in elliptic equations is considered in the class of -vector fields. The optimality system is characterized and the convergence of the gradient method is proved. To apply the SQP-method to the singular optimality system, a modification involving a feasibility step in the primal and dual variables is introduced. The resulting algorithm has a second-order convergence rate. Numerical experiments are included.