|Abstract:|| In this paper we address the numerical approximation of the incompressible Navier-Stokes
equations in a moving domain by the spectral element method and high order time integrators. We present the Arbitrary Lagrangian Eulerian (ALE) formulation of the incompressible
Navier-Stokes equations and propose a numerical method based on the following kernels: a Lagrange basis associated with Fekete points in the spectral element method context, BDF time integrators, an ALE map of high degree, and a robust algebraic linear solver.
In particular, the high degree ALE map is appropriate to deal with a computational domain whose boundary is described with curved elements. Finally, we apply the proposed strategy to a