This paper develops an adaptive finite element method for shape optimization in stationary incompressible flow with damping. The continuous shape gradient of an objective
functional with respect to the boundary shape is derived by using the adjoint equation method and
a function space parametrization technique. A projection a-posteriori error estimator is proposed,
which can be computed easily and implemented in parallel. Based on this error estimator, an
adaptive finite element method is constructed to solve state and adjoint equations and a regularized
equation in each iteration step. Finally, the effectiveness of this adaptive method is demonstrated
by numerical experiments.