An efficient two-step algorithm for steady-state natural convection problem.

In this paper, we propose a new highly efficient two-step algorithm based on local Gauss integration for the 2D steady-state natural convection problem. The basic idea of the algorithm is to compute an initial approximation for the velocity, pressure and temperature based on a lowest equal-order finite element pair P 1 – P 1 – P 1 , then to solve a linear system based on a quadratic equal-order finite element pair P 2 – P 2 – P 2 on the same mesh. Next, we give the corresponding stability and convergence of the algorithm, which show that the new two-step algorithm has the same order convergence rate as the quadratic equal-order stabilized finite element method. Finally, some numerical examples show that the new method is efficient, reliable, has good precision and can save a lot of computational time compared with the quadratic equal-order stabilized method. [ABSTRACT FROM AUTHOR]