On the numerical approximation of a geometric control problem

Abstract

The purpose of this paper is to introduce a new method for solving an optimun design problem: determining the aerodynamic body of minimun-drag profile at constant velocity in a viscous incompressible fluid. The stationnary Navier-Stokes problem (in velocity-pressure formulation) is discretized by menas of a mixed finite element method. In some particular cases, the existence of solurions allows us to prove convergence results.