Resumen de A new stabilized finite element method for shape optimization in the steady Navier-Stokes flow

Zhiming Gao, Yichen Ma

• This paper investigates shape optimization of a solid body located in Navier�Stokes flow in two dimensions. The minimization problem of total dissipated energy is established in the fluid domain. The discretization of Navier�Stokes equations is accomplished using a new stabilized finite element method which does not need a stabilization parameter or calculation of high order derivatives. We derive the structures of discrete Eulerian derivative of the cost functional by a discrete adjoint method with a function space parametrization technique. A gradient type optimization algorithm with a mesh adaptation technique and a mesh moving strategy is effectively formulated and implemented.