Decoupled two level finite element methods for the steady natural convection problem

In this work three kinds of decoupled two level finite element methods are proposed and analyzed for the natural convection problem. Firstly, some a priori bounds and the optimal error estimates of velocity and temperature in L 2 norm are provided for the standard Galerkin finite element method. Secondly, by using the coarse grid numerical solutions to decouple the nonlinear coupling term, we establish the convergence results for the proposed decoupled two level finite element schemes with meshes h and H satisfy h=H 2. Finally, two numerical examples are presented to show the efficiency and effectiveness of the proposed algorithms for the steady natural convection problem.