Streamline diffusion finite element method for stationary incompressible natural convection problem

In this article, a streamline diffusion finite element method is proposed and analyzed for stationary incompressible natural convection problem (NC). This method is stable for any combinations of velocity, pressure, and temperature finite element spaces, without requiring inf-sup condition. The well-posedness and convergence (at optimal error rate) of this scheme are proved in terms of some conditions. Numerical experiments are illustrated to validate our theoretical analysis and show the streamline diffusion finite element approach is effective for solving the NC problems.