Spectral discretization of the Navier–Stokes equations coupled with the heat equation

Abstract

We consider the spectral discretization of the Navier–Stokes equations coupled with the heat equation where the viscosity depends on the temperature, with boundary conditions which involve the velocity and the temperature. This problem admits a variational formulation with three independent unknowns, the velocity, the pressure and the temperature. We prove optimal error estimates and present some numerical experiments which confirm the validity of the discretization.