Summary: We are concerned with the problem of the stationary, potential, subsonic flow. Firstly, we formulate the mechanical problem and the associated minimization problem with constraints, in a functional space \(W\) endowed with a certain norm. Section 2 contains the main original results. A density lemma for the space \(W\) is presented, then is introduced a stable, convergent, internal approximation of \(W\). We state the approximate minimization problem and prove a convergence theorem. A minimax problem coresponds to the approximate minimization problem with constraints (\(P_h\)). For this one, we deduce the existence of the saddle point, using a separation Hahn-Banach theorem. In the end is presented an iterative algorithm for determining the minimax point.