Shape optimization of Stokes flows by a penalty method

Shape optimization in incompressible Stokes flows is considered based on the penalty method for the divergence free constraint at continuous level. Shape sensitivity analysis is performed and numerical algorithms are presented. An iterative penalty method with reliable accuracy is used for solving numerically the penalized state and possible adjoint. The iterative penalty method as an inner solver is more efficient than the standard mixed finite element method in 2D. Asymptotic convergence analysis and a prior error estimates for finite element discretizations of both state and adjoint are provided. Numerical results are presented to show the effectiveness of the numerical optimization algorithms.