On the convergence of spectral approximations for the heat convection equations

Abstract

In this paper, we focus on the convergence rate of solutions of spectral Galerkin approximations for the heat convection equations on a bounded domain. Estimates in $$H^2$$ -norm for velocity and temperature without compatibility conditions are obtained. Moreover, we give rates of convergence for the velocity and temperature derivatives in $$L^ 2$$ -norm.