ON DISTRIBUTED H1 SHAPE GRADIENT FLOWS IN OPTIMAL SHAPE DESIGN OF STOKES FLOWS: CONVERGENCE ANALYSIS AND NUMERICAL APPLICATIONS

We consider optimal shape design in Stokes ow using H1 shape gradient ows based on the distributed Eulerian derivatives. MINI element is used for discretizations of Stokes equation and Galerkin finite element is used for discretizations of distributed and boundary H1 shape gradient ows. Convergence analysis with a priori error estimates is provided under general and different regularity assumptions. We investigate the performances of shape gradient descent algorithms for energy dissipation minimization and obstacle ow. Numerical comparisons in 2D and 3D show that the distributed H1 shape gradient ow is more accurate than the popular boundary type. The corresponding distributed shape gradient algorithm is more effective.