  In this paper, we study the problem concerning the approximation of a rigid
obstacle for flows governed by the stationary Navier-Stokes equations in the
two-dimensional case. The idea is to consider a highly viscous fluid in the
place of the obstacle. Formally, as the fluid viscosity goes to infinity inside
the region occupied by the obstacle, we obtain the original problem in the
limit.
  The main goal is to establish a better regularity of approximate solutions.
In particular, the pointwise estimate for the gradient of the velocity is
proved.
  We give numerical evidence that the penalized solution can reasonably
approximate the problem, even for relatively small values of the penalty
parameter.
