Spectral discretization of the Navier-Stokes problem 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 confi rm the interest of the discretization.