On an effective approach in shape optimization problem for Stokes equation

In this paper, we deal with the numerical study of a shape optimization problem governed by Stokes system. More precisely, we propose an effective numerical approach based on the shape derivative formula with respect to convex domains using Minkowski deformation (Boulkhemair and Chakib in J Convex Anal 21(1):67–87, 2014). Then, we present some numerical tests including comparison results showing that the proposed algorithm is more efficient, in term of the accuracy of the solution and central processing unit (CPU) time execution, than the one involving the classical shape derivative formula massively used in literature.