Two-level variational multiscale method based on the decoupling approach for the natural convection problem

This paper enfolds a detail analysis for two kinds of two-level variational multiscale method for the natural convection problem. Firstly, from the finite element variational multiscale (VMS) method based on two local Gauss integrations (LG-VMS method), the two-level LG-VMS (TLG-VMS) method is proposed. Then, the decoupled two-level LG-VMS (DTLG-VMS) method is presented by combining the decoupling approach to reduce the computational complexity and scale. Stability analysis and error estimation are given. Finally, numerical results confirm the theoretical analysis and the effectiveness of the proposed methods.