Optimal shape design for Stokes flow via minimax differentiability

This paper is concerned with the shape sensitivity analysis of a viscous incompressible fluid driven by Stokes equations with a nonhomogeneous boundary condition. The structure of the shape gradient with respect to the shape of the variable domain for a given cost function is established by using the differentiability of a minimax formulation involving a Lagrangian functional combined with the function space parametrization technique and the function space embedding technique. We apply a gradient type algorithm to our problem. Numerical examples show that our theory is useful for practical purposes and the proposed algorithm is feasible.