  One of the crucial aspects of patient-specific blood flow simulations is to
specify material parameters and boundary conditions. The choice of boundary
conditions can have a substantial impact on the character of the flow. While
no-slip is the most popular wall boundary condition, some amount of slip, which
determines how much fluid is allowed to flow along the wall, might be
beneficial for better agreement with flow patterns in medical images. However,
even if one assumes the simple Navier's boundary conditions on the wall, in
which the relationship between tangential components of the normal traction and
the velocity is linear, the determination of the specific value of the slip
parameter is often difficult.
  In this work, we present and test an optimal control method to estimate
Navier's slip parameter on the wall and the velocity profile at the inlet using
artificially generated flow domain and flow data. The results show that it is
possible to recover the flow patterns and Navier's slip parameter by using
sufficiently accurate discretization even from data containing a substantial
amount of noise.
