The computational approximation of solutions to inverse problem in fluid-dynamic is often a formidable task. A general inverse problem can be seen as Partial Differential Equations (PDE) constrained optimization problem. Most of these problems for which the solution of direct problem depends on a single or multiple parameters. Historically, parametric optimal control problems are a powerful and elegant mathematical framework to fill the gap between observed data and model equations to make numerical schemes more reliable and accurate for prevision, especially in Finite Element approximations. In optimal control problems, although widely exploited by various branches of scientific research, it is necessary to minimize a functional cost dependent on the state variables of the system, through the control of one or more variables that influence the solution of the state problem.