A finite element method for phase-field dependent topology optimization in Stokes flow

This presentation is concerned with finite element approximations of a phase-field parameterized topology optimization problem governed by the Stokes equations. The discrete minimizing phase field is sought in the usual conforming linear finite element space while the nonconforming linear finite elements (Crouzeix-Raviart elements) and piecewise constants are used to approximate the velocity field and the pressure field respectively. Convergence of the resulting finite element method will be discussed for the uniform and the adaptive mesh refinement strategies respectively.