A numerical method for drag minimization via the suction and injection of mass through the boundary

We study the problem of minimizing the viscous drag on a body via the addition or removal of mass through the boundary. The control considered is the mass flux through all or part of the boundary; the functional to be minimized is the viscous dissipation. We use Lagrange multiplier techniques to derive a system of partial differential equations from which optimal, i.e., minimum drag, solutions may be determined. Then, finite element approximations of solutions of the optimality system are defined and optimal error estimates are derived.