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In this article, we consider the two-level stabilized nonconforming finite element methods for the stationary conduction–convection equations based on local Gauss integration. The proposed methods are applied to solve conduction–convection equations with a special relationship of coarse mesh and fine meshh = H/3 to avoid the coarse-to-fine intergrid operator. The methods involves three different corrections: Stokes correction, Oseen correction, and Newton correction. Moreover, the stability and convergence of the proposed methods are deduced. Finally, numerical results are shown to validate the theory analysis and demonstrate the effectiveness of the given methods. [ABSTRACT FROM AUTHOR]

We present and analyze two categories of efficient decoupled methods for the unsteady incompressible natural convection equations in this article. The proposed methods include first order, second order standard form and rotational form, and are extended to any order schemes. Some consistency items are added to help complete the stability analysis, and they disappear in non-discrete space. Finally, the correctness of the theoretical analysis and the effectiveness of the given methods are verified by several numerical experiments. [ABSTRACT FROM AUTHOR]