Spectral discretization of time-dependent vorticity–velocity–pressure formulation of the Navier–Stokes equations

Abstract

Abstract In this work, we propose a nonstationary Navier–Stokes problem equipped with an unusual boundary condition. The time discretization of such a problem is based on the backward Euler’s scheme. However, the variational formulation deduced from the nonstationary Navier–Stokes equations is discretized using the spectral method. We prove that the time semidiscrete problem and the full spectral discrete one admit at most one solution.

Keywords

• Nonstationary Navier–Stokes equations
• Vorticity–velocity–pressure formulation
• Implicit Euler’s scheme
• Spectral discretization