Spectral discretization of the time-dependent Navier-Stokes problem with mixed boundary conditions

Abstract

In this work, we handle a time-dependent Navier-Stokes problem in dimension three with a mixed boundary conditions. The variational formulation is written considering three independent unknowns: vorticity, velocity, and pressure. We use the backward Euler scheme for time discretization and the spectral method for space discretization. We present a complete numerical analysis linked to this variational formulation, which leads us to a priori error estimate.

Keywords

• time-dependent navier-stokes problem
• mixed boundary conditions
• implicit euler scheme
• spectral method
• 35q30
• 65m70